Then, perhaps, I will try readjusting the power supply voltage. Mac Repair & Upgrade Secrets (hereafter MRU&S) says that the SE power supply is auto-adjusting, although there is a voltage pot for manual override.
I'll try that and see what happens (I don't think it'll blow anything up!)
If that doesn't work, then I'll have to look at testing and replacing any components whose impending failure could show this as an early symptom.
c