I had the same symptoms with my TBolt a couple of weeks ago with it powering off and not wanting to stay on for extended periods on battery power. I checked my battery status and noticed 2 problems: 1. low voltage (around 3.8mv) 2. Battery status was Unknown (should say either charging or not charging)
The low voltage output was causing the phone to shutdown whenever something that demanded extra power would fire up. Fortunately for me I bought backup batteries for my phone way back when I first got it and realized battery life wasn't the TBolt's strong suit.
I put in a new battery and all my problems disappeared. The new battery shows the proper status and is putting out 4.1mv
Just a thought.