it could be 2 reasons this is happening. i've been through both.
1. you could be pulling more power than your alt is charging the battery. when this happened to me, my system quit working. i found out later when i parked my car that it wouldn't start later because my battery died. may not be the cause, but it is probable.
2. you talked about voice coils heating up. if you blow a voice coil in your sub, it will short circuit the amp, causing it to shut off briefly. it usually happens when you hit a real low note in the music you are listening to, making the sub hit hard causing the short. if you can listen to it for a while at a real low volume and it doesn't happen, then that would be your problem.