Its happen to the two srt-10s we own in my family. Interestingly enough, it only happen when new... over time it sorts itself out.. i know you dont want to hear this... but even if they replace it under warranty, the new unit is going to do the same damn thing.
The fix in the short term is to not listen to it so loud, at some point i had figured out exactly what the max amount was I could listen to it, without shutting off, but then once everything "burned in" it all seemed to work great. Might have taken a few k miles though.
Keep in mind the speakers are a bit "tight" too when new, so it takes a while for them to break in, and before they do that, it requires more volume/amps to push them .. once they break in, it'll all sound better, and take less power to make her crank.
Jon
PS. when it cuts out, you can either turn it off for about 20 minutes, OR you can actually leave it on, and the volume will return once the amp cools off.