This happened with my wife's phone. It cutoff at 20% every time. It ended being all the "other" storage on her phone that you see in the bar at the bottom of iTunes. This included all of her text messages with attachments as well as emails, app storage etc. All this stuff stores on your phone over time. I reset the phone back to factory settings and set her email back up and had to download her apps again, but it fixed her battery problem right away.