Why does my monitor keep cutting out?

This could simply be a cabling problem. Check that your video cable doesn't run too close to anything like a power pack, or something else that could cause interference to the signal.

OK; since I'm the OP I'll elaborate: the DisplayPort cable had slipped, and was directly next to my (powered) USB hub. Simply relocating the cable solved the problem completely. I guess with a digital signal, some kinds of interference can have a significant effect, requiring a signal reset.