So I just kept cycling power and... it has been powered on for over 2 hours now with no problems.
I'm beginning to suspect the electrolytic caps. Being el-cheepo (no-name) brand, they probably went intermittent short or low ESR and blew the fuse. After replacing the fuse (remember it's been over a year since this thing has been powered on for more than a few seconds at a time) the caps needed a little time to reform.
Or maybe a power surge popped the fuse (and the cap re-form thing still applies).
I think I'll replace the caps -- for peace of mind -- and see if it continues to work.