iPhone 6S (iOS 9.3.2) starts switching off whenever battery is low
This happened to me when my iPhone 5 battery died. If it's less than a year old, take it to an Apple Store or Authorized Reseller for replacement.
If it's older and you don't have an AppleCare plan, you can buy a compatible battery from eBay; I did and has worked great for over a year. 

It may even happen that Apple replaces it for free if it's a batch of defective batteries (mine was, but I replaced it before the announcement.

You can check the health of your battery with coconutBattery if you have a Mac.