Arduino leave PWM on
Why not create a global brightness variable (e.g. cBrightness) so that you can adjust the brightness accordingly when the time comes? With a global variable, you can still maintain the brightness of the LED even after it exits the start() function.

For the start() function, you can include one argument (int/bool type variable) in the function to determine when to perform the brightening or dimming of the light depending on the RTC timing. 

void start(int st)
{
  if(st==0)    
  {
     //Brightness decrement function here
  }else if(st==1)   
  {   
     //Brightness increment function here
  }
}    


For the brightness decrement function, it is the opposite of the increment function:

for (int i = 255 ; i &gt;= 0; i--)
{
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
}


To summarize, the code could look something like this:

#include &lt;DS3231.h&gt;

//Set Variables
int fadeTime = 15; //Fade Time
int onHour = 12; //Light On Hour
int onMin = 00; //Light On Minute
int offHour = 19; //Light On Hour
int offMin = 00; //Light On Minute
int led = 9; //Set pinout with with PWM
int cBrightness = 0;  //Current brightness

DS3231  rtc(SDA, SCL);
Time t;
void start(int st);

void setup()
{
  pinMode(led, OUTPUT);
  rtc.begin();
}

void loop()
{
  t = rtc.getTime();

  // Send Day-of-Week
  Serial.print(rtc.getDOWStr());
  Serial.print(" ");

  // Send date
  Serial.print(rtc.getDateStr());
  Serial.print(" -- ");

  // Send time
  Serial.println(rtc.getTimeStr());

  if (t.hour == onHour &amp;&amp; t.min == onMin) //Check Time
  {
    start(1);
  }else if (t.hour == offHour &amp;&amp; t.min == offMin)
  {
    start(0);
  }
  //Maintains brightness
  analogWrite(led, cBrightness);

}

void start(int st)
{
  if(st==0)     //Will decrement in brightness
  {
   for (int i = 255 ; i &gt;= 0; i--)
   {
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
   }
   cBrightness = 0;

  }else if(st==1)   //Will increment in brightness
  {   
   for (int i = 0 ; i &lt;= 255; i++)
   {
    analogWrite(led, i);
    delay(((fadeTime * 60000)/306));
   }
  cBrightness = 255;
  }    
}