Sounds like your modem does not isolate your handset/telephone when it goes Off Hook.
Some handsets grab a little power from the line every now and then to keep any internal memory alive. When this happens it can disrupt the server which may toss you off. Try unplugging the handset.
Also make sure call waiting is disabled. This will toss you off too.
My server seems to go to sleep for long periods. I can wake it up by going to Outlook Express and regularly clicking on Send/Receive. When it reacts I can go gang busters for a while until it fades away again.
Also have you line checked from the exchange.
Hope that helps.