From what I have seen on my empeg, it's fairly sensitive to transients. i.e. when a heavy load is switched on the negative going spike on the supply causes it to think the supply is going down. No problem with the engine running but running off battery only and I sometimes have this problem. A cap should fix this. Silkysmooth is correct in saying that if the voltage is continuously low then you have other problems. From memory the empeg switch off voltage is around 8.5 volts. If your system is getting that low then you have greater problems.

A possible other fix would be to provide a small amount of averaging on the low voltage input detection circuit. I'm guessing that as soon as it goes low for one sample the player will restart. If the empeg say checked for 10ms of continuous low voltage and [u]then[/u] shutdown, a lot a the problems might go away. Can someone who knows the hardware comment on this? It might even be possible in Hijack if the sampling is done in kernel space

We had similar problems with ESD testing on a project here at work and this sort of averaging fixed the problem quite well.