Does anyone else ever use a Mac to connect to your projector setup?
This could be a somewhat different problem...
The Mac uses an automated system which uses the secondary data channel to the display, DDC, to query the DISPLAY for its capabilities, and sets the resolution according to what the DISPLAY reports it can attain. In this way, those pesky, error-prone humans do not get into the loop to mess up the settings.
Sometimes when using Switches, splitters, and similar devices, the device simply does not answer. When using a Mac, no answer from the device means you get no display, because none was detected.
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You MAY be able to change this by making certain that the EDID signals from one projector/display are connected through the splitter back to the input connector at the PC or Mac.