Update : we have the same problem with flat displays than with video projector : if we boot with a display connected to the Radeon DVI port, and then unplug it, when we replug it we get nothing; if we plug a display on the vga port, we get the desktop.
It looks it is the standard Windows 7 hot plug detect behavior that cannot be removed on the Windows side.
It seems that some NVIDIA card can be forced to keep some EDID / Display resolution, but not this ATI one.
An EDID emulator device should do the work, as the MonitorDetectKiller device too.
It seems there is also a solution with the Display Changer II software.