The first thing I can think of is to go to control panel, device manager, choose your NIC, right click it, go to Power Management, and ensure that "Allow the computer to turn off this device to save power" is
NOT checked.
Have you tried a driver update? Head to your motherboard manufacturer's site and download and install the most up to date driver they have available. Make sure you uninstall the old driver first before installing the new, either through the add/remove programs screen if it's available, or through device manager if it is not.
If the hardware itself is damaged, there's nothing you can do short of buying a PCI expansion LAN card and installing it into a PCI slot or replacing the motherboard.
http://www.newegg.com/Product/Produc...82E16833156139
Something like that should do you fine. Look for a 10/100 card if you don't have a gigabit router, though, unless you want your computer to be "future ready."
Do you have a non Windows software firewall installed? Does Windows report the adapter is disconnected or disabled, while your connection is down, or does Windows think everything's okay?
When it goes down, try pinging the localhost loopback, 127.0.0.1, if you get a response the problem is probably hardware related and not software.
To ping the loopback, start > run > cmd (or just start > cmd on Vista/7) and type ping 127.0.0.1
Edit: This is all, of course, assuming you use Windows. If you're on a Mac I can't help you.