Make sure your computer isn't going into sleep mode or anything. And when the WMC disconnects after a few minutes, check your computer to see if an of the sharing services had stopped. Also, check your event viewer and see if it lists why your pc disconnected your xbox.
Additionally, Try this fix from microsoft:
http://support.microsoft.com/kb/934542
You might get lucky...
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These walls fall down around me but I will stand
And though my body be burned away I will live