Internet drops out randomly - "The Default gateway is not available"

I am running Windows 7Ultimate. My Internet connection keeps getting dropped, and when I run the troubleshooter, I can get two different messages: "Troubleshooter Couldn't identify the problem" or "The default gateway is not available." When I get the first, I might as well give up getting on the Internet. When I get the second, the problem can be fixed. Any amount of time later, my connection is dropped again. It can be a day or just an hour

Is this computer the only one on the network? I assume your computer is set to DHCP aka getting an IP etc from your router?