PowerPC :: G4 Turns Itself Off / Shuts Down Unexpectedly

I've a MDD G4 dual 1.0 along with the wide acrylic-bezel 20" Mac monitor with the light in the lower right corner. Yep, it's starting to look ancient. But I still have much use for it EXCEPT that it has a very nasty habit of turning itself off catastropically in mid-thought, as it were. Oddly, this behavior comes and goes in spurts. it will hit hard for a couple of weeks then a couple of months will pass with relative peace and stability. Then, back to the crisis.

Sometimes I get a warning from that power-on light in the bezel -- it might flash brighter for an instant, then within a few seconds the whole system loses power just as if I'd turned off my power strip. Other times, it pops in and out of sleep mode for several cycles, but usually this ends the same, with no power at all. Odder still, the machine has a tendency to turn itself on unaided. This can happen even after a controlled shutdown. It turns on, acts normal for 20 minutes, then maybe goes to sleep and wakes up a couple of times, then crashes. No intervention at all on my part at any time. This is not a software shutdown of any controlled variety. Anyone know what's happening? I can't tell you how much gnashing my teeth have endured.