the Tripplite OMNI1000LCD UPS which I had raven (my server) plugged in to was still shutting off on me. at this point, I had one computer, 1 ethernet switch, 1 ethernet hub, and a kvm switch plugged into the battery. it should be able to handle that. then I moved the little stuff off battery, leaving only the computer. Even then, I've had it power off.
Today I exchanged the UPS for another one (same model) hoping that perhaps the one I got was bad. if this one shuts off on me too, I'll have to get a refund and go get a different kind of UPS. I've again plugged in 1 computer, the ethernets, and the kvm switch into it. we'll see.