I have a similar battery problem on my wife's 2-month-old iPhone 6+. Here are the symptoms:
1. The phone would not charge beyond the displayed battery percentage, which was 7% in this case. The battery kept draining no matter how long we kept it plugged in.
2. The displayed charge value declined over the course of the day until it came to rest at 1%, after which it only went back to 4% when I connected it to my pc and iTunes started up. That's about it.
3. I did all kinds of reset as found here in the forum. None worked.
4. I backed up the phone using iTunes and did a restore using iTunes. Then, the pc kept making these connect/disconnect sounds and eventually iTunes told me that the device had malfunctioned and couldn't be recognized and needed to be reconnected.
5. At this point I noticed that the phone was caught in the shut down/power up loop. I disconnected from the pc. The loop went away and I was able to set up the phone. Still wouldn't charge past displayed figure- 3%.
6. I plugged in phone all night until morning. Nothing changed. So, I decided to let the phone battery die out so that I could try the hair dryer idea.
7. The hair dryer worked- TEMPORARILY! After blowing hot air on the back of the device for about 3 minutes or so I immediately plugged in the dead phone. The apple logo appeared immediately and the phone booted itself up and showed 100% charge. After about 20 minutes I disconnected the phone from the wall and it died within 10 minutes! I tried the drier a couple more times. Each time, after I plugged in, the dead phone showed the apple logo on and off (like a looped thing) until the phone booted up again, only to show the persistent 1%. It was at this point that it occurred to me that it was strange for a dead phone to start up when plugged in; it should show only the battery icon or something like that along with indication of charging in progress.
8. So, I went online again and found this web page: https://www.mendmyi.com/blog/2014/06/has-your-iphone-5-died-and-wont-charge-or-c ome-back-on-we-can-fix-that/
Their explanation of matters makes sense. They had me examining all the Apple adapters and USB leads at home- we have accumulated quite a good number over the years. I found one cable that didn't pass muster on closer inspection. And it had, by some strange accident, recently been used to charge that ailing iPhone. Wow!
And that got me thinking. Why haven't I found some sort of "official" explanation of the problem, along with its cause, from Apple? Why? Oh, why have the 'isheep' been left seemingly without a shepherd?