I suspect there's probably a faulty batch of batteries. Wouldn't be the first time.
Similar thing happened to the iPhone 5 I had. Charged to 100%, ran fine up to about 20-30%, and then shutdown out of the blue. When it first started to happen, I would turn it on and the battery would be reported as under 5%. Charged it back up to 100%.
Took it in. They plugged it into a Macbook Air and ran some fancy diagnostic tools and showed me the results. The graph they showed me was a detailed history of the battery discharge, and when it got to between 20-30% left, it dropped right off a cliff to 0%. So, given that data, they had me do restore and setup as new, and told me that if it happened again they'd replace the phone.
Couple weeks later, I went in and they replaced the phone. Replacement worked fine when I still had it, and I've since handed it off to a family member and got a 6 Plus. They still have that phone, and it's still working just fine.
[doublepost=1453958192][/doublepost]
I guess you could suppose, but you'd be wrong. I know of 6 people off the top of my head, that have iPhone 4s's and 5's that are still in use today. None of them have lagged in iOS9, up to and including the latest release (9.2.1 at this time.)
