An intermittent connection can be a pain, but if the light flashes that shows it's losing the physical connection to the exchange. So generally you'll want to go through the standard tests.
How is the phone line? Any noise or crackling there? Try dialling 17070 option 2 for a quiet line test. Noise there indicates a phone line fault, which you'd need to report to your phone provider-plusnet or whoever.
Second, move the connection to the test socket. You access this by removing the faceplate on your master socket and plugging the system into the socket behind-as it's intermittent you'll need to leave it there for a bit to see if it makes a difference.
Third if possible is try alternative hardware-switch the filter and if possible the router-though I'm aware not everyone has a spare router lying around!
Of course it'd also be worth getting hold of tech support to test the line too-possibly one of the staffers here may pick this up and do that for you but being a weekend it may be quicker to bite the bullet and wait in the call queue and get this done before you start disassembling things.
