Try this (echoing what profdlp said above).
Start> In search box type
device manager> Enter
Expand
Universal Serial Bus Controllers> For each controller named
USB Root Hub, right click the listing and choose
Properties> Click on the
Power management tab> See if
Allow the computer to turn off this device to save power is checked
If so, try unchecking it and see if your PC will now keep the monitor connected.
A Guy