Internet connection lost when receiving mail

When receiving mail via Broadband landline the Internet connection is lost. About 2 to 5 messages come through and then Internet and DSL lights go off on modem and connection is lost. Once I manually connect to network and click on ‘Send and Receive’ all messages come through as normal. If Mail is then left unused for a period of maybe a half hour, the same thing happens again.

I am using the full version of AVG, with AVG Firewall activated and Windows Firewall turned off (I think). Windows Mail had previously worked fine on the same machine. The problem happens only when receiving mail.