Andy is right, but my modem runs fine off an extension.
My main socket is downstairs, but I wanted broadband and a phone upstairs (and keep the other phone downstairs), so I ran a normal phone extension upstairs and attached the splitter and the modem. In the phone socket of the splitter is a 2-way adaptor with a phone and another extension all the way back downstairs.
It's a clumsy system, but a fortunate side effect is that it keeps the cable from splitter to modem short, so maybe that's the key.
One more thing, I've had extension cables that work fine with a phone (so you think the lead is fine), but they fail to engage properly with the modem socket, giving exactly your symptoms.