Ha! online gaming and a modem? is it a dialup connection? 56k?
Well one of the problems could be your modem and the ISP you are using- they may not be compatible. Has this system been working fine up until recently, or have you always had this problem with it? if it has worked in the past, then your modem might be dying.
You might need to try a different manufacturer of modem, or switch to another ISP.
The other posibility is that another program in the background is mucking up things. if you can please post up a list of your system specs, and any/all software you are running at the time of the disconnect/problem- this should include whatever is in your startup list as well.