After reading through this, one of the posts suggested to me that the monitor can't handle the switch from mains to UPS power. There may be a few cycles of dropout that causes the monitor to reset.
If, that's hte case the solutions are:
1. replace the monitor
2. Replace the UPS to a constant on variety. i.e The devices always run on synthesized power
3. Try a constant voltage transformer. These device do change the waveform to somewhat of a square wave, but they generally will help with slight sags. They are large, ugly and EXPENSIVE. So ebay would be a good source. **broken link removed**