Same problem here. Had mine about a month or more, and the problem started just before Christmas. Randomly freezes then reboots. Thought it might be because of rooting, but others with non-rooted ones are having the same problem.
Just before it happens, the system slows down a lot. Returning to the home screen sees it taking quite a while before the app icons appear. At that stage I have tried removing the running apps by swiping them from the list, but it is still just a matter of time before it freezes and reboots again. Should I be taking this thing back to the store?
BTW, I have been using a cover with a magnet ever since I got my Nexus 7, so could that really be an issue?
Tim