I only have a couple of data points on this so far, but I thought I'd check if anyone has run into anything like this before:

Yesterday I installed WinCompose, and it seems to be working fine. However, that night, I noticed that my PC wasn't automatically turning off its screens like it usually does; I rebooted the system in case something bizarre happened, and waited a while longer, and saw that it still wasn't shutting off the screens after the requested amount of time... Then, remembering the one change I'd just made to my system, I right-clicked WinCompose's tray icon and chose 'exit', and then waited again, and this time the monitors went to sleep as expected.

This has happened to me before with other programs -- some IM clients seem to cause it, though I've only ever left those running by accident; this is the first time it's happened to me with a program that I would otherwise intend to permanently leave running. I wasn't watching the entire time that I was waiting for the screens to turn off, so I'm not certain yet whether they were completely failing to turn off, or just turning off then immediately turning back on... I'll do some more experiments, but I just thought I'd check whether anyone has any leads for what would cause this.