This discussion seems to have run its course, but I wanted to mention one other thing that happened recently.
After a long day out of the house, I wanted to use Maps to ensure a cab driver was taking the best route with the least traffic. At 20% left, upon opening the app, the iPhone shut down. Either the phone crashed, or it went into this early shutdown mode.
Unlike sometimes when you try to turn it on and you get the bootup screen (white background black apple logo), this time it gave the battery dead screen (black screen, empty battery, and lightning plug), so I was out of luck. Out of stubborness, I tried a few more times over the course of 5 minutes to no avail. However, the remarkable thing, when I arrived at my destination 10 or so minutes later I tried again and it did power on. I forget what percentage it stated, but I think it was close to where it left off, probably between 10 and 15%.
This is most likely a fluke and doesn't add/detract from anything mention before, but I'm stating this as a just in case. Who knows, in an emergency situation this could be vital information.