Hi there, I was facing exactly the same problem that has been discussed here.
After replacing my battery on my iphone 5 the battery panel got frozen (it updated
only when restarting the phone) and the phone rebooted constantly when it
was charged.
Here is my solution: I had my battery being replaced by a local shop
(NOT an authorized apple dealer) and when the problem occured I
brought back the phone multiple times to the shop. The guy in the
shop was quite collaborative, so he tried one battery after the other
(there were original apple batteries, at least there were packed like that).
Anyhow, after putting in the third or forth battery the problem stopped.
So, my solution is, replace the battery, and if that doesn't work, send back
the battery and have it replaced by a new one and try again. It seems
that these batteries are somewhat fragile.
Good luck with your solutions.