Restore it as new not from back up and use it like that for a few days to see how it works. If it is ok, then restore from back up and see if the problem returns.
Mine did a similar thing, it would be at 35% for a while and suddenly went down to 5 or even 1%. After, it started to shut off at 12%. I re-calibrated the battery but it only worked after the first full charge.
I ended up swapping it at a Genius bar because the home button got loose, but when I explained the genius about the battery problem he told me that it wasn't right and if the replacement one started to behave similar that most likely that my back up was corrupted and needed to restore as new.