Unfortunately, when the is set once, the option remains set until the next time you are downloading mail and uncheck it. If you find that you are being disconnected as soon as your mail is checked, this is most likely the problem. This opens the Send and Receive box. For good measure, if this box is already unchecked, quickly check it, and then uncheck it. This may even be the case with new modems.
Modems tend to generate heat, which can cause flaws in the electronic components.
If all else fails, you may wish to try installing a new modem.