The Short Version: The UPS’s USB connection had been inadvertently shared with the virtual machine. Setting it to only be accessible by the host OS (OS X) solved the problem.
Recently I noticed my virtual machine instance under VMWare Fusion (3.1.3) seemed to be running unusually slow on my Mac. Yesterday I noticed that the status indicator for my battery backup kept appearing and disappearing in the menu bar.
While inspecting the energy settings for both OS X (Lion) and Windows 7 (VM) I decided to check the connected USB devices for the virtual machine. Sure enough, my CyberPower UPS was showing as connected to to the Windows 7 guest OS. I have no idea how this happened. There’s no reason I would have intentionally connected the USB interface for the my UPS to to the VM. Perhaps I clicked on it when intending to connect a different device at some point.
Regardless, as soon as I disconnected the UPS from the VM both systems started functioning at a more normal speed and the status indicator stayed in the menu bar instead of restarting.