OK, try setting a static IP, if you do not know how to do this, go into your connection settings..
If it is XP, right click the two screen in the bottom right, go to properties, in the properties box, there are a few check boxes, go into the settings for TCP/IP and set a static IP, you must set one for your network, so go into command prompt, hold Windows press R, type cmd, press enter. in there type ipconfig, in there you will get your IPv4 address, follow the 3 numbers shown first (mine would be 192.168.0. ) and change the last number to something. Test this for awhile on your system with a static IP, do note, it can cause conflict with other devices that have dynamic addresses, the DHCP may try and assign that IP to another computer, knocking you both off the network.
for vista/7, right click the two screens with the little earth, also beside the time, click Network and Sharing centre, in there, you will see your current connection, click View Status, in there, same idea as above, you will see TCP/IP, go in there, set a static IP..
If you have already tried this, you never mentioned it, it is hard to go by what you have tried and what you have not with such minimal information.
Another thing you could try is, download a program called WireShark, let it run while you are using the internet, after it drops, stop the test, and take a look at what happen when you disconnected... It's a semi-difficult program to understand but it may give you some sort of hint.