zoochaser,
from your description it sounds like it could be related to your line quality or settings. Especially if the same thing happens with different providers.
Here's a zip file with information about line quality and settings that can help.
ftp://http://www.wrightwoodcalif.com/forumimg/TelephoneLineQuality.zipI wouldn't bother with the files about FCC complaints.
Here's an important point that I've used numerous times that helps resolve the frustrating disconnects.
After you've checked all your computer settings and interior wiring of the house and continue to have problems, then it's more than likely line quality causing the problem.
Your testing must include removing "ALL answer machines, fax machines or portable telephones from your home telephone system.
Never call the phone company and complain about a modem connection as it won't do you any good.
What you need to do is call the phone company and complain about intermittent static on your line, that causes you to be dropped from phone conversations. Again, I repeat.. Don't even mention a computer or modem and the key words are "intermittent static".
By using that phrase they can't come out and charge you, but you must make sure your interior wiring is good and wired correctly or may be charged for a service call.
If after a few complaints they don't fix it demand they switch your pair of wires.
For instance in Wrightwood there is a squirrel problem that affects many lines in town. A squirrel eats through part of the wire insulation and as soon as moisture is in the air, the connection becomes shorted and intermittent. Thus causing dropped modem connections and also static on your phone line.
Good luck and keep us informed of your progress.