LED fade class strobes for unknown reason
I added some Serial.print() statements to your code to point out the bug:

This is the modified LED::changeLed() function I used:

void LED::ledChange() {

  /**/Serial.print(brightness); 

  // Flip LED change value between brightening and darkening
  if ( brightness &lt;= lowest || brightness &gt;= highest ) {
    change *= -1;

    isNeg = checkNeg(); // Determine if we're brightening/dimming the LEDs

    // A 1-in-25 chance to change the fade-rate
    if ( random (25) == 13 )
      changeChange();

  }


  brightness += change; // Adjust the LEDs brightness

  analogWrite( pin, brightness ); // Brighten/darken the LED

  /**/Serial.print("\t+ ");
  /**/Serial.print(change);
  /**/Serial.print("\t= ");
  /**/Serial.print(brightness);
  /**/Serial.print("\t");
  /**/for (int i = 0; i &lt; (brightness / 5); i++) Serial.print("*");
  /**/Serial.print("\n");
}


I marked the additional lines with /**/.

Here is a piece of the serial monitor output, where the bug occurred.  The columns are organised as follows: brightness before the function changed it + change = brightness at the end of this function. The * lines graphically represent the LED brightness (i.e. the last number); this allowed me to run your sketch without a physical LED, at much higher speed (I deleted the delay(60) in loop()).

183        +    3         =    186  *************************************
186        +    3         =    189  *************************************
189        +    3         =    192  **************************************
192        +    3         =    195  ***************************************
195        +    3         =    198  ***************************************
198        +    3         =    201  ****************************************
201        +    3         =    204  ****************************************
204        +    3         =    207  *****************************************
207        +    3         =    210  ******************************************
210        +    3         =    213  ******************************************
213        +    3         =    216  *******************************************
216        +    3         =    219  *******************************************
219        +    3         =    222  ********************************************
222        +    3         =    225  *********************************************
225        +    3         =    228  *********************************************
228        +    3         =    231  **********************************************
231        +    3         =    234  **********************************************
234        +    3         =    237  ***********************************************
237        +    3         =    240  ************************************************
240        +    3         =    243  ************************************************
243        +    3         =    246  *************************************************
246        +    3         =    249  *************************************************
249        +    3         =    252  ************************************************** #####
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    1         =    252  **************************************************
252        +    -1          =    251  **************************************************
251        +    3         =    254  **************************************************
254        +    -3          =    251  **************************************************
251        +    3         =    254  **************************************************
254        +    -3          =    251  **************************************************
251        +    3         =    254  **************************************************
254        +    -3          =    251  **************************************************
251        +    3         =    254  **************************************************
254        +    -1          =    253  **************************************************
253        +    1         =    254  **************************************************
254        +    -1          =    253  **************************************************
253        +    1         =    254  **************************************************
254        +    -1          =    253  **************************************************
253        +    1         =    254  **************************************************
254        +    -1          =    253  **************************************************
253        +    1         =    254  **************************************************
254        +    -1          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -2          =    253  **************************************************
253        +    2         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    1         =    255  ***************************************************
255        +    -1          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************
254        +    2         =    0  
0        +    -2          =    254  **************************************************


The bug begins at the line I marked with ####. I'll try to narrate the events from the point of view of your function, starting from line #### (1):


Is brightness 249 in range? yes -> don't invert sign | add 3 | return
Is brightness 252 in range? no -> invert | change fade rate? yes, new fade rate = ±1 | add -1 (we just inverted the sign) | return
Is brightness 251 in range? no -> invert (here's the bug!) | change fade rate? no | add +1 (ve should subtract, but we just inverted the sign...) | return
It continues like that until a fade rate change occurs, oscillating between 251 and 252. That looks out like a constant brightness.
The fade rate increases and the oscillation values change, maybe approaching 255 (if the smaller value goes below 250 the led will continue to behave properly, but that's not our case).
Another fader rathe change causes the program to make brightness greater than 255 (in our case 254 + 2). And if you add 2 to a one-byte unsigned variable holding a value of 254 you won't get 256 (the variable can't hold that value) but 0. That's something called "integer wraparound", as Majenko pointed out in his comment to your question.




So, that was a long description of a very simple problem.
To solve it you cold for instance prevent the brightness value to be greater than 250 and smaller than 5 adding two lines to your ledChange function:

void LED::ledChange(){
    // Flip LED change value between brightening and darkening
    if( brightness &lt;= lowest || brightness &gt;= highest ){
        change *= -1;

        isNeg = checkNeg(); // Determine if we're brightening/dimming the LEDs

        // A 1-in-25 chance to change the fade-rate
        if( random( 25 ) == 13 )
            changeChange();
    }


    /**/ if(brightness &gt; highest) brightness = highest;
    /**/ else if (brightness &lt; lowest) brightness = lowest;

    brightness += change; // Adjust the LEDs brightness

    analogWrite( pin, brightness ); // Brighten/darken the LED
}