[eru]

I guess, if they survive any power cut at all, they are probably not taking their time cues from the main's frequency. I agree with your wager that they probably run on low-voltage DC and perhaps have a capacitor somewhere to bridge short outages.

Where do you live that you have frequent enough brown outs to notice these things?

I have a time switch. It looks entirely mechanical, but I suspect it gets its time signal from the mains: it doesn't seem to drift at all. If there's ever a power outage (which happens from time to time when our breaker trips, not because the real mains is down) it just stops advancing the time, but doesn't reset, because it's all mechanical.