It is hard to tell without all the facts but this sounds like the classic
microfilter problem . With broadband on a phone line there are 2 services
running over that line .When these services reach the premises they need to split in order to work properly. For this you use a microfilter ,the microfilter
plugs into the phone socket and has 2 connections ,one small for the Broadband router or modem the other a standard phone socket.
This is all straight forward until you have a extension phone line or a Sky box,fax machine etc. In this case you often need another microfilter or more to ensure the services never meet. If the 2 services meet the broadband is normally the service that drops.
We hope this is of help
Kind regards
Naims.co.uk