Here is a good explenation for why you may be having connection problems and tips to help out your situation. Your connection to an ISP involves similar steps as connecting to any other modem-accessable service and is subject to the same potential problems. Call waiting bumps you off the line when someone else tries to call you, but it is easy to fix. If that does not solve your problems, it may be errors with your modem init string. Click here to for init strings and how to add a string to your modem.
Line noise is perhaps the biggest single reason for dropped lines.
Understand that the local phone company doesn't guarantee that the normal voice lines running to and from your house will be suitable for modem use. The lines they give you are supposed to be able to pass most sounds in the 300Hz to 3000Hz range. Normally, there is no more than a -10db loss of signal from the local telephone office to your standard jack. Most users connect at these rates every day. There are several conditions that can degrade the signal quality on standard phone lines.