I have spent the last 6 months trying to understand and fix the constsant re-booting of my BThub4 but have at last fixed the problems! Hooray!!.
For some reason the BT help lines do not give this info, so I will, because I think it might help a lot of people to resolve their faults.
After several phone calls to the tech support people who checked my line and tried various fixes which did not help, they sent me a replacement hub, which also did not fix the problem.
So the problem was either caused by connections to the router or interference from other sources. After much trial and error I have located and fixed the problems.
1. Panasonic plasma tv (I thought it was the youview box, but no). Whenever it was switched on it randomly created interference that caused the hub to re-boot. I put ferrite cores at each end of the youview box ethernet cable, that fixed it for a while.
2. Then it started again but much worse. It turned out to be the central heating boiler igniter system suppressor had failed. I found it by tuning a MW radio to no channel and every time the boiler thermostat caused it to fire up the igniter circuit created some unbelievably bad noise! So I replaced the boiler electrical parts and a miracle, no more re-boots.
It wasn't a BT hub problem at all.
I hope this helps some of you get to the bottom of your re-booting problems..