Well if the sub amp is the only amp cutting out then the fault in the wiring for the sub amp or the amp itself.

Does it play for short times? does it get hot?

Probable causes if the sub amp drops out but comes back on on it's own could be:

Short between speaker terminals or even loose wiring in the sub enclosure. I have seen dual voice coil wiring come loose and short the amp sending it into protection mode.

In systems using AGU fuses (the glass fuses about the size of a pinky) I have seen people push them so hard that the contacts spread out and only one end is actually holding the fuse the other one either has intermittent contact or is floating entirely away from the contact and the amp has no power, Systems using Maxi style fuses are usually not tight enough to hold the fuse properly or heats the contacts to the point that it causes issues. So look at these points.

Also look under the hood where the amp power is connected for anything obvious.

Look for grounds that are loose and make and break contact. Look for a loose remote turn on wire (it's the small gauge wire next to the large black and Red (or blue or whatever they used)

The amp could have a failure.

If the amp gets hot but plays a while then shuts off then takes a while to turn back on chances are there is either not sufficient ventilation, or the amp is driving a load lower than the recommended, which will cause it to overheat.

Jeff