Apple admits there is a battery problem.
They finally went public and have offered, through December, 2018, to replace the faulty, quick draininig batteries for $29 instead of the usual $79.
Apple's Battery Replacement Options
One tiny detail: if you want to bring it to an Apple store for replacing, you may be waiting awhile for an available appointment. And for some iPhone owners, they were not able to get anyone to answer the phone at the store(s) when they called, forcing an online attempt to schedule an appointment.
Some stores are busier than others, so depending on your ability to wait, you may be driving to a store a little further away, than usual. And if you don't want to drive further, your patience will eventually be rewarded with a new battery, but Apple cannot determine when.
Yes, there are THAT many batteries to replace. Keep trying... or do what a Tutor client did: they bought a newer iPhone. A bit pricey to solve the battery problem, but they got instant gratification!
ALWAYS REMEMBER: before calling for help - is it plugged in, and is it turned on?