Decent chance the capacitors in the PSU have had it due to old age and general junkiness. I believe that unit hailed from when Antec was using capacitors best defined in terms of excrement.
Even if the PSU isn't at the heart of the problem, I think I'd replace it. My guess is that it's the issue though.
Another possibility is that the motherboard's battery is right on the edge of being out of juice and randomly drops low enough that the BIOS loses some, but not all, of its settings.