I've the exact same problem. However, my battery is at 100% and I can always get to the verifying of security blah blah and then it shutsdown. Other times I can use the phone for various amounts of time. From minutes to a couple of days. I've upgraded from OS v4.2 to the latest OS v4.5 something. This didn't help my problem.
If an answer could be provided to this most annoying problem I would be well chuffed.
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