sub cuts out when I accelerate from a stop

That's certainly an odd problem. Not many factory Jeep radios had preamp outputs so it's possible the sub is connected to the radio's speaker outputs and not dedicated preamp outputs. Check to see if any other speakers cut out. If they do, the problem is either in the radio itself or the wiring to the speaker(s) that cuts out. If only the sub is having problems, try running new signal cables from the head unit to the sub's inputs to rule out wiring problems. It's a longshot, but also check the alternator's regulator and voltage output as the engine revs - there's the possibility that the voltage is not being regulated properly and that's causing the sub to go into protection mode.