This has been happening to me on my 5S for months. The Genuis bar cannot see it on the diagnostic (ie no sudden decrease spike) so it must be that the battery meter is messed up, i guess. It is incredibly frustrating.
Just wanted to update on this. I had a separate issue with my screen popping up (from the battery expanding) and called Apple instead of going in. The rep said something that lead me to thinking. I booked a genius appointment and had them do a diagnostic. Turns out, what I thought (and what the Genius Bar thought) were sudden battery depleations were actually the phone rebooting due to repeated system errors. They replaced the phone on the spot.