Well, first off the modem is not a hardware modem it is a software modem. You are not the first person to have "issues" with these modems. They are buggy, just like windoze.
The best thing to do is to get a external serial modem that is hardware based. USB modems are not much better than what you have either. Stick with a external serial and you will have a LOT less trouble.
If you need help finding one, let me know. I'll be glad to search for you one. I could also suggest you call a local computer place to look for a used one. I went to my ISP and got a old U S Robotics modem for $10.00 and it works great. I also like all the lights on the front too.
Maybe someone else will come along with a fix but I wouldn't count on it.