I have an iPhone 5 that has had battery issues since this summer. Sometimes, the phone dies in a "low battery-esque" way anywhere in the interval: [0,60]%. Charging it for a minute or so allows the phone to boot with the same battery level again. I updated to iOS 7 a couple weeks before the AppleCare on the phone expired, and this seemed to have mitigated the issues for a while. However, now they have appeared again a month or so after the warranty expiring. How well does Apple honor these type of cases? Do I have a $900 brick on my hands or do I have chance on actually getting a working phone?