Modem stays off hook

I have an Agree 56k modem that stays off hook. If I unplug the modem the phone line works, but as soon as I plug it back in, it is off hook again. Reinstalled modem and drivers to no avail. Does this even with computer off, and also with modem physically out of computer.
This is the third Agere modem that has the same probem. A new modem works for 2 to 3 weeks and then starts the problem. When I change modems, I do not have to make any changes to the software. Just plug in the new one and it works.