My iPhone 5 usually shut off around 14-17%, other times I would make it to 1%. I have had this happen on iOS 6 and iOS 7. I went to the Apple Store, ran diagnostics and was told that my battery was normal at 84% health, above the 80% threshold that would constitute a warranty battery replacement. It made sense that if my battery was at 84%, it would shut off at around 16%, 100-84=16. The "Genius" told me to do another restore and set up phone as new (I had already done this once but it was not from recovery mode), turn off background app refresh and other features. I restored as new, no background app refresh, no spotlight indexing, no airdrop, no motion and everything seemed normal thanks to some midday charging, because I would not let my phone get below 20%. Today I was at a store and was using my phone when it shut off at 37%. I was able to find a lightning dock and set my phone on it, it turned on immediately, left it there for about 2 minutes and continued using it. A few minutes later, pin wheel and phone shut down. I called Apple support as soon as I got to a charger. Ran diagnostics, and battery still operating "normal". Was told to restore AGAIN, set up as new, but use phone without downloading any apps or music to see if problem persisted. Why would I even use it? How am I supposed to drain the battery without any apps? I am supposed to use it with only the operating system for 24-48 hours. If it is normal then the problem is supposedly caused by apps that I can then load on and test 1 by 1 each day! That is ridiculous, I thought the apps were supposed to be tested for stability.
Their answer to my problem is to turn off the features of this feature-rich phone. They tout the huge catalog of the App Store but I cannot use any of them. It is not like I am running an iPhone 4, less than 60 days this was the newest, most current hardware. This is unacceptable.
I have another appointment at the Genius Bar tomorrow to run more diagnostics. I am sure they will tell me I am SOL and turn me away as usual.