Daze - If your deck is only running RCA's out, then this is strange. Usually you see this situation when the deck amplifier is driving some speakers and one of the speakers has cooked, thus shutting down the deck. The same situation can happen to big amplifiers as well.

Heat kills electronics. If your deck is getting overly hot, then either something bad internally, or when the heat reaches a certain point the deck is protecting itself. this could be a situation where the deck is just tired and needs to be replaced.

If I where in your shoes, I'd probably isolate the deck from the amplifiers (i.e. tower/cabin/sub) and turn it on for awhile to see if it heats up and cuts out. Same test could be done with your stuff connected to it. Your only driving line level outputs so it shouldn't take a real long time to reach normal operating temps.

As mike mentioned, if you have battery issues in the scene then that should be addressed first. Feel free to hit me up on phone. I think you got my digits. Can walk you thru a couple of things...