I don`t think you can pinpoint the HomeHub as the problem on this evidence. It is more likely to be an intermittent line fault causing the router to drop the BB signal. I suggest you report it to BT and see what they say.
I have had similar issues with my line over the past week and have done all the tests such as changing the filters on the line, plugging it into the master socket, swapping the router and letting PlusNet (Part of BT and cheaper!) test the line. An engineer is coming this morning to physically test the line locally. They are also bringing a spare router just in case - now that`s what I call service.