We have a spare Homehub thanks to BT's amateur approach to troubleshooting. Had a similar situation a few months ago, although ours was a continuous lack of internet rather than frequent drop-outs. None of our routers (all different manufacturers) could get on the internet...despite this BT insisted on sending us a new one. The day it turned up the original magically started working before I'd even got the new one out of the box - there had been a problem at BT's end affecting a number of customers. As previously I hadn't had any problem at all with the original Homehub, I left that one in place.
They will send you a plastic bag in which to return your old router, but nothing actually telling you you have to return it, so don't, and you'll have a spare one!