I have a 6s and have been having this problem for quite a while. Phone shuts off when there's about 20-30% battery left, although it can vary. When I hold power button it says plug it in. When I press home and power it comes on, shows 30 or 48% battery or whatever and after 5 seconds shuts off.
I tried a full dfu restore and it didn't work. I went to the apple store and they checked that my hardware/battery were just fine. The guy said I was the third person today with the same problem and that he expects it to be corrected shortly with an update. One of their suggestions was to drain the battery completely, however this was impossible due to the problem.
FINALLY I tried running down the battery with the flashlight and it WORKED. Battery drained all the way and it doesn't shut off anymore.
Important note: you can't use any other programs. I tried making it drain faster by turning on netflix and the flashlight--it shut off as usual. You need to turn on the flashlight and just put your phone down and don't touch it. Once it drains, charge to 100% as normal. If I remember correctly I had to do this two nights in a row and have since not had problems.
Hope this helps, pretty annoying problem to have.