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My iphone drains quick sometimes all the way down to 1% and sometimes it shuts off with 40% battery. In either case when i plug it in it comes back at a higher battery percentage. Ive tried factory restoring then restoring with icloud backup it seemed to work ok for a couple weeks but then issue came back. This seems to have happened to 2 of my iphone 6 phones after updating to 9.2. When i was on any version of 9.1 all was good.
Could be a software thing. Or, could just be a bad battery. From what, I’m not sure. But it does sound like your battery needs to be replaced Labor iPhone 6 Battery Replacement Parts iPhone 6 Battery
I had a similar issue. Replaced the battery and had no more problems.