You do not have call waiting disabled.
Line noise does cause disconnections.
You have a fax modem on the same line as your modem and it is trying to receive faxes which will disconnect the modem. Do not stay idle for more than 15 minutes. If you do, all you need to do is reconnect. If this is a problem for you, call us and sign up for a dedicated account. If you have call waiting, you definitely need to disable it.