"The problem I've encountered is that for most of the small-ish UPSs, that when the batteries go past their useful life, the UPS starts cycling the power, even if the wall power has been steady on. APC is particularly nasty about this for certain models."
Most UPS will cycle the batteries periodically to test them. They keep the mains ready on standby in case the test fails, but the idea is that the batteries need an occasional "stress test" to help cycle them and to make sure they still work. It's when this test fails that the UPS reports the problem.
My issue is that UPS management software sometimes acts funny. I had it completely drain out an UPS once for no apparent reason which is why I don't hook up an UPS's communication channel anymore and simply go by its built-in display.