There's nothing wrong with your modem. All laptop internal modems and most desktop internal modems are called "controllerless", in other words, they use the CPU to control the modem. Your external modem has its own little CPU to run the communications.
So these controllerless modems are more prone to drop a connection. Maybe they're just trying to tell you to drop the dialup connection for good.
My Acer Tavelmate 2301 LCi can stay on the for hours no problem, other times it will just drop the dial-up connection no reason it seems. My old desktop on the same line and dial-up with an old external modem never drops the connection. So something is up with this notbook. I'm running Win XP Pro. I've tried new cables. Very weird. What could it be? My ISP can't help and Acer tested the machine and said it's fine. Yeah right.