Your UPS might not have the capacity it once did, and can no longer keep the wattage high enough to power everything...
If it's more than a couple years old, it might be time to replace the UPS (or at least replace the battery/betteries.)
Also, make sure that ONLY the items you need to keep running are connected... Computer, external HDDs, ... things that would be hurt (data loss, etc.) by suddenly losing power. You might lose the game, but the monitor doesn't need power during a power outage... better to keep the machine running than lose data just so you can see your character die. Same for network, the USB pet rock, and the iPod charger.
(Modern UPSes have two parts - one powered and one protection-only... put all the...