If your dial-up connection is suffering from constant hang-ups or difficulty signing on, there is a good chance you have developed a phone line problem, or, your modem software is not working correctly with your modem. Have you noticed the problem being worse since the rains have come or when it is very damp? This could point towards a problem with phone lines, possibly even a problem with your "phone box" that resides on the outside of your home.
If it is a phone line issue, there are some things you can check yourself; insure all your phone lines are in good shape, if you are sharing the phone line you use for the internet with other telco devices (fax machines, answering machines, etc.) try disconnecting them and connect to the internet with just the computer plugged in to see if this helps. You can also look through your outside phone box to make sure the connections are clean and are not covered with spider webs that are wet, etc., this can cause shorts in your phone system and reduce the quality.
If none of the above seem to be the issue, you may want to try to contact the manufacturer of your modem to see if there is possibly a newer driver for it that may help improve it's functionality.