I went to the Apple Store today, had my diagnosis done, and am in line for a battery once they become available.
Like others, I don't believe the cause is really the battery (or, at least not solely the battery). I can always get my phone to shut down within 1 hour of usage even if I start with a full charge.
Here is my test scenario:
1) Start with a fully charged 6S (purchased just over a year ago, usually charged once a day (overnight)).
2) Go outside. Go for a walk.
3) While walking, listen to podcasts using Overcast. read Twitter using Twitterrific. Phone will shut off with no "low battery" warning within one hour 100% of the time. I don't run. I walk. I complete just under 3 miles usually on this one hour walk.
The problem started THE DAY I loaded iOS 10.0. I've taken the same walk 5 to 7 days a week (when in town) for the last three years. I never had this problem before loading iOS 10.0.
If I attempt to power up the phone, I get the "battery is drained, please plug it in" image. Once I plug it it, the phone will boot after 10-30 seconds. The phone will display approximately the same remaining battery percentage it showed when it died. I have had phone die with as much as 65% battery remaining. It will almost always die before it gets down to 40%.
Something about this combination is a problem. I can listen to Overcast without running the screen for an hour without issue. Having the screen lit seems to be related.
I can walk on a treadmill for an hour using the same Apps, but on WiFi, and the battery will drain normally. If I get to 20% I will get the low battery message.
I can drive in my car for an hour (so not on WiFi) using the same apps, and battery will drain normally. If I get to 20% I will get the low battery message.
Just some additional data points. I will be very surprised (but pleased) if the problem goes away with a new battery.
John