There were some other similar posts (that I can not find now) with a suggested solution that worked for me on my iPhone 5. Before 8.1.3 my battery lasted all day easily, after 8.1.3 it dropped like rock. The posts suggested some kind of infinite loop retry related to the iPhone trying to access an account (the ones under Settings > Mail,Contacts,Calendars > ACCOUNTS). The suggested solution was to log into https://appleid.apple.com/ (I did this from a laptop) and update the password if prompted to, because the current password was not secure enough. I logged into my apple id and was not prompted because my password was secure enough. I then logged into my wife's apple id (that I access from my phone) and was prompted for a more secure password (bingo). I made this change last night and my iPhone 5 battery is back to normal; it is like day and night. I guess it's possible Apple fixed something on their end at the same time; whatever, it working great now!