Cornwallis
When I upgraded to the 'up to 8MB' Tiscali package I had a very similar problem - in my case it was because the original [Tiscali supplied] Sagem 800 Modem which I'd used on the 'up to 2MB' package wasn't up to the job and it either dropped the connection or I couldn't get on line at all.
I solved the problem by installing a Netgear DG834PN Router and I've had no problems whatsoever in getting on line nor have I had any dropped connections since.