Can you provide more details? What operating system are these computers running? Are there multiple domains? Are you logged into the domain or the local machine?

Also check to make sure Windows isn't powering down your NIC (which is the default) to save power.

On Windows 2000/XP, right-click "My Computer" > "Manage" > "Device Manager"

Double-click on "Network Adapters" and right-click on your NIC. Choose "Properties" and click on the "Power Management" tab. Uncheck the box labeled "Allow the computer to turn off this device to save power." Click OK, close the MMC, and reboot.

Normally, if there's no activity over the network on that device (from your machine) for a certain period of time, Windows will "shut off" the device.