Update: The issue has reared its head again. It is looking more likely that I will have to do a full restore and not restore from a back up. I have noticed something curious though. Turning on low power mode leads to the the battery discharging all the way to 1%. Interesting...
Over the last few months I was seeing an unusual bug in iOS where by my iPhone would power down even at ~ 30% charge remaining. I managed to get the issue resolved after a quick visit to the Genius Bar but not before I tried every other trick in the book.
The issue arose a few months back while I was on the Public Beta for iOS 9.3. My first attempt to fix the issue was to remove myself from the beta once iOS 9.3 was made available for general release. The issue persisted. My next step was to go through the battery calibration steps. Again, the issue persisted. As a last resort before visiting the Genius Bar I restored my iPhone, again the issue lived on but I should mention that I restored from an encrypted backup. Looking back, this was never going to do any good given the root of the problem.
My next thought was that the battery itself was the issue, so I set up a Genius Appointment. The Apple Genius ran the usual diagnostics from which I was expecting to see a less than healthy battery. As it happens my iPhone 6 battery still has 84% of its original capacity. What the diagnostics did show up was a high level of third party and system applications crashing in the background. As there were no apparent hardware issues the next step was to wipe the device and start from scratch. Before doing so the Genius suggested the possibility that just wiping the settings back to the default might work. If not, I could go ahead with the full device restore myself.
As it happened, restoring just the settings worked in my case. The Apple Genius's theory was that carrying backups from phone to phone, which I have done since the 4S, resulted in something getting messed up in the background and the OS was tying itself up in knots until it shut itself down. Who knows, but if you are having mysterious shut-downs, restoring your settings could be worth a shot.