Some warranty programs are 3 years now for select batches.
Very grateful for the link you sent but alas I am out by 11 months. Not eligible.
Update 9:
Well after hosing my daughters iPhone 5 again by re-installing the backup for all of my daughters stuff, I thought I would get on the horn with apple and run the diagnostics on my particular battery. So what I have is a 4 year old battery which was capable of lasting about 36 hours, but it seems that when the 10.1.1 update was run it developed the problem.
I did a Recovery Mode Factory restore and the phone seemed to be working as it had before the update. Lasting 30-36 hours on a charge in standby. But with the backup re-installed, the phone died inside of 3 minutes and the faulty indicator would say it was charged 100% again.
So Apple ran the diagnostics remotely that are in update 10.2.
My battery came back as faulty with only maximum of 20% charge capability.
Apple Store will do the change out of the battery for $79 bucks.
But that is 2 1/2 hour away. Apple does have an authorized hardware repair in our area, but when I called it was $112.
My instant reaction was Yikes. But upon cooling my head off a bit I realize that they get charged a certain amount by Apple and have to recover their tech cost and make a modicum of money. Plus it saves me 2 1/2 hours in the car or days of sending it in to Apple. So instant gratification at a premium for living in the Awesome place I do with no Apple Store. Trade off.
So tomorrow I will drop the phone for repair and pick it up in the afternoon. Repair is less than 1 hour.
Also will pick up Apple Care + for the new iPad Pro and a Smart Keyboard and nice glass screen protector. Expensive day, but peace of mind will be had.
Great thing is my daughter will be thrilled that her phone will last longer than her old mans or her other sisters phone.
Here is what the Tech said when I asked what he thought was going on with the phone and why I was able to Factory Restore my phone and it was able to function for so long.
About the factory Restore...... "That is a bit odd and it likely refreshed the phone enough to act normal until the deterioration of her battery started to become more apparent to you both. Either way it’s clearly the battery failing so it needs a repair to work appropriately from here on out."
I will update once the new Battery is installed and report on function of the phone at that time.
Remember ... this is nearly a 4 year old battery that has been well used first by my wife and next by kids who are very hard on phones in every way.