I had this exact problem.I had experienced it before so strongly suspected what the problem was.The trouble was no-one would listen to me and,like you,kept telling me their was no problems(which there obviously were!).
In my case I am a few miles away from my exchange and maybe you are too ? This means that your line cant carry the same speeds as other people closer to the exchange but it keeps pushing itself too hard and struggles to keep up so basically every now and then the connection drops out to 're-sync' itself.It should lower the speeds to make your line more stable but as most people are on 'up to' connection speeds it keeps re-connecting at the fastest possible speed and so inevitably drops again and again and again.....
It took me many months of questions to BT and my ISP before I finally got it resolved.In the end,BT(who had told me my line was fine) changed a couple of things with my line and all is now fine.The things they changed were to do with background noise and interleaving/interweaving(whatever that is).
Hope this helps.