Hi,
I had a similar problem using AOL dial up. Random disconnects all over the place.
It turned out to be a problem with noise on my phone line - a 20+ year old twisted pair copper line.
I switched to a cable telephone line and the problem never happened again.
I've also heard that certain modems (like Diamond Supras - the make I had at the time) can disconnect if there is an incoming call on your phone line.
Given all the problems I had with dial-up, I would strongly recommend you get Cable Internet if the cost/availability is okay where you are.
My flat rate AOL access used to cost me 15 GBPounds a month (about $20?) but for an extra 10GBPounds (about $13) a month, I get more than 12 times the bandwidth and near bulletproof reliability (only 2 outages of less than a half-hour in the past 5 months).
Hope this helps.
Best Regards,
Kit