How do you connect? Ethernet or wireless? If Ethernet, try another cable (they are cheap, and not very rugged). Try another port on your router, if you using a router.
In Device Manager > Network adaptors, right click on your adapter, select Properties > Power Management and untick in the top box. If that does not help, tick it back.
If it seems to happen after the same time of idleness, say 15 minutes, this might apply: Network Idle Session Time to Automatically Disconnect - Vista Forums