This happened to my iPhone 5. I took my phone into Apple and talked to a genius. She checked the phone and said it looked like a software bug. She could tell because hardware checks indicated the battery was ok and checking the 'Battery' option in Settings showed the 'usage' and 'standby' times weren't displaying anything. The fix was to do a DFU recovery and setup the phone as a new device, i.e. do not use a previous backup.
10/30/15 at 6:24am