Tim writes:
It could well be that you have had a series of bad UPSs, or it could
be
that your mains supply is so bad that the UPS spends most of its time
supplying the computer, rather than charging its batteries. Or you
could be putting too much of a load on it.
Nah, it was the UPSes :-) Have three others nearby, some of them a few years
old, chugging away.
Did some Googling, found a few discussion threads in the last month, talking
about the exact problem I had, the exact same brand slowly discharging its
battery, even though it had mains power. Looks like this manufacturer had
some bad luck recently, with their quality control.