> The UPS batteries are still good, at least as far as I can tell.
Suggest testing. Quick and dirty way to see how many minutes your gear will last off a power supply. You don't need to boot up into windows just switch on the PC and press the BREAK button then pull out the mains from the battery. Then set your stop watch, however long you get divide that by 2 and subtract the average shutdown time of your PC, and that's the time you should allow before automated shutdown.
Also your UPS software should have something to diagnose battery capacity issues.
Ta