Slow fade option with an LM3914 IC
The "fade" that the datasheet mentions is fading between successive LEDs in DOT mode only.  It has nothing to do with how fast the LEDs respond to the incoming signal, but how the change in signal is represented.

For instance, an increase in input would be represented as:

.....
o....
O....
Oo...
oO...
.O...
.Oo..
.oO..
..O..


etc (. = off. o = dim, O = bright).

I think what you are wanting by your description is a slow fall-off of the signal, not a "fade".  That is where the display shows the latest peak value and then gradually drops down.

For that you would need a peak detector with sustaining circuit.  That would take the incoming signal and compare it to the current maximum value, and if higher then set the current maximum to the new value.  Over time the current maximum would reduce itself.  The bargraph module would then be representing this stored peak value instead of the actual signal value.

The "sustaining circuit" could be created with a capacitor with a bleed-off resistor (the time constant of the RC circuit defines the decay rate).  A circuit involving comparators could probably be built for the peak comparing.