I cant see why an amp would die because the power cable is too small. You would simply be restricting the amount of power the amp is getting. I can see over-voltage being a problem for an amp, but it should tolerate a bit of under-voltage. When the amp turns off it takes time for the capacitors inside the amp to discharge, and they will continue to supply a lower voltage as they discharge. If the amp died because of under-voltage you would kill the amp every time you turned it off.
I dont think running power cable thats too small will directly blow an amplifier, but seeing as the amp was going into protect everytime a decent bass tone hit (when the amp is pulling max current) then i would say the voltage is dropping below 10.5v or whatever its protection is set on. Anytime an amp goes into protection isnt good and the protection function is there for a reason...to protect the amp.
Edit; milkandjuiceonlycomein2litres - you say you had a 50A fuse on 10awg cable...thats should have been 30A, if your power cable had a short in it after the fuse it wouldnt got really hot and possibly caught on fire before that fuse blew. Take a look at the fuse on the amp, i would imagine it wouldnt have been 50A, maybe 30-40A. Thats a good way to determine what fuse you should be using at the battery, by adding up the fuse/s on your amp/s.