A reminder window appears with the option to remain connected or not, and if I don't do anything, it disconnects me without my wanting it to.

http://img576.imageshack.us/img576/9593/picture1zhk.png

This occurs about every 3-5 minutes.

(Mac OS Help)
http://img233.imageshack.us/img233/8797/1oshelp.png

Go to:

Network Options
Then to:

PPP Options
http://img815.imageshack.us/img815/7065/3modempppoptions.png

Put "0" minutes in the "Prompt every __ minutes to maintain connection", then deselect it. This now seems to eliminate the unwanted prompt.