Try Start>Control Panel>Network Connections and right click the LAN connection then properties. On the General Tab you should have the name of the Adapter, click configure. Now the configure settings vary by manufacturer so forgive me if this isn`t exactly right - Go to the power saving tab and try unticking the box that says allow the computer to turn off the device for power saving. There may also be a setting under the advanced tab called "link down power setting".
Also on the original properties tab (before you clicked configure) select the box that says Notify me if this connection has limited or no connectivity) See if the above makes a difference and post back.