So, after some advice from here and elsewhere on my previously described hi-fi problem, I figured I’d try disconnecting the speakers one by one to see if I could isolate the problem. I loaded the offending Dr Who DVD, stuck the intro music on a repeat loop, and began fiddling.
First I reconfirmed the problem. The first thing I figured out was that it only occurred with the volume turned up above a certain level. Below about -30dB on my amp’s volume scale, no problem. Above that limit, the amp kept switching itself off at loud parts of the music.
Next I disconnected the left main speaker wires at the rear of the amp. Turned the volume up… and the amp stayed on. I reconnected the left speaker wires, turned the amp up… real high, to about -15 dB (way louder than we ever play anything), and it stayed on! I played with it a bit more to confirm the behaviour.
So, it looks like the wires connecting the left main speaker to the amp were somehow slightly unstable in their connection. Taking them out and reconnecting them seems to have completely solved the problem. I presume the wires were at some point close enough to be sparking or otherwise shorting when a loud bit of sound was being sent to the speaker, resulting in the amp circuit-breaking itself in self-preservation.
Yay! Thanks to all who suggested trying this.