I am having a similar problem to the one described in the BT community forums:
http://community.bt.com/t5/BT-Infinity/HH3-constantly-dropping-broadband-Weird-BT-Speedtest-Results/td-p/457057/highlight/false
speed is fine, but the connection drops every 15 minutes or so. This happened two weeks ago just as I was starting my semester of online teaching - unbelievably inconvenient.
I was pleased that I had an engineer round with 24 hours when this first happened. He checked everything in my house and could find nothing wrong. The following day I was supposed to have a visit from a wholesale engineer, but he never came, or at least not to the house. I think he might have done something locally, but basically it was then fine for two weeks, and now same problem again - connection dropping every 15 minutes. Total nightmare - I teach online and it's a disaster. I've opened another issue with BT and it's being investigated ... maybe I should get them to send me a new router - but if 2 out of 3 of these Hub 3.0's are faulty ...
Just requested a new router, and am told I am on some 18 hours wait thing to see if changes they have made at the exchange will "settle". BB is now permanently off.
The BT Net options of a dedicated copper line seem ridiculously expensive given that it would only offer a slower speed. Am wondering what to do ...