I had exactly the same problem with BT. 9 times out of 10 my connection would fail within 5 minutes of initially connecting. Generally the service would be better after re-connecting, but I still had a lot of random disconnections.
Nothing I tried improved the service. It was suggested to me that it might have been caused by a fault with my telephone line.
I doubt this because I've been with a different ISP for the past few weeks, with far better results.