If it keeps dropping because the connection theres not a lot you can do apart from maybe start a ping to keep the connection from falling idle. type start>run>ping -t www.google.com to start a ping and keep the connection active.
I'd try a different access number first. You also might use a trial version of a different ISP just to make sure it's not the ISP you have being wonky. You can also have the phone company come out and check the line for problems. The last thing I can think of is to replace the cable from the PC to the phone line.
Do you get any error messages at all? It's possible you have the "blaster" worm, if I recall correctly. That d/c me every five or so minutes.
Please download HijackThis . Create a folder at C:\HJT and move HijackThis.exe there. Run a scan and save the log file. Post the whole log file here. Do not fix anything since most of them listed there are harmless (some are system required). This program will help us determine if there is any spyware/malware on your computer. Please post these results. Also, please post with your ISP, type of account, make and model of modem in use.
The blaster worms not that nice. It restarts your computer like the sasser not just disconnecting you.