Well, first off, as I said, this is not a laptop. It's a tower (desktop) PC attached to an Uninterruptable Power Supply. So laptop-specific solutions aren't the answer. Nor is the problem likely to be hardware related as I have two Vista installations on this PC and one is affected and the other isn't. Thanks for the suggestions anyway.
Secondly, both installations of Vista are using the same drivers, i.e. the MS ones that come with Vista. I've run this setup for a couple of years, with no problems at all on previous installations.
Anyway, after 36 hours or so of not working, the power settings have once again decided to notice there is indeed a battery connected and start working properly again.
I hate intermittent issues that appear from nowhere and then go away, but I guess I'll have to wait for the problem to come back (if it ever does) and have another go at fixing it then.