A couple of various thoughts:
1)Can you test these three pieces (preamp, amp, speaker) separately? Do you know if they work properly when paired with other equipment? From the description here, I'd look most closely at the power amp. If the sound cuts out, then that's probably the protection circuit tripping and you might suspect the speaker cable or speaker for a short as gregbump mentioned. But, if you're hearing distortion prior to it cutting out, that's more indicative of a problem in the power amp. The best test here is to try another power amp that works and see if the problem goes away. If that's not it, then swap, speaker and preamp until you find the source of the problem. No, this isn't easy unless you have access to a lot of gear, but it's the only way you'll isolate the problem.
2) Try running in regular mode instead of bridged. When you run in bridged mode, you'll get more power, but there's more opportunity for problems and overheating (which will lead to the problems you describe). It also has the effect of halving the impedance of your speaker (if you have an 8 ohm speaker, it will look like a 4 ohm speaker to the amp in bridge mode). Lower impedance=more power, but will easily overheat your amp leading to distortion and triggering the protection circuit. Doing this may be easy or hard depending on the kind of cabling you're using (e.g. banana plugs will be easy, modifying a 1/4 jack or Speakon less so).
3) Be sure to check the easiest thing - make sure the cabinet is working properly with another amp. Steal your guitarist's amp for this test - it doesn't have to sound great, but you do want to run it pretty loud to see if it's causing the amp to misbehave. But be careful not to kill your guitarist's amp if the speaker isn't really the problem.
4) It's possible that the preamp may have a problem as well - failed power supply regulation might cause DC to come out on the output which would freak out the power amp and cause another shutdown.
5) For the least noise at output, you basically want to set the preamp level relatively high and use the power amp gain control to control overall volume. This will minimize the amount of noise when you're not playing. But if your preamp tonally sounds different at different output levels (varying levels of distortion for instance), then set the preamp gain to the tone you want, and adjust the master output level with the power amp gain. The power amp level setting won't have any appreciable difference in the output tone for most solid state amps.
Good luck,
David Fung
