I have an Xperia Z1 (1 year old, not rooted) and it has never done it before. I was playing Pokemon Go (just downloaded it), i was messing around in it for around 5 minutes and suddenly my phone turned off becouse of low battery. The game is not officially out in my country so i downloaded the .apk from a site. (Others didn't have a problem with it) The phone was kind of hot and it's 35 °C here so i don't think that helps the situation. I plugged in the charger and turned it back on and it started optimising applications on boot. Deleted the game, downloaded AVG and ran a virus scan. It didn't find anything. I will do a batery calibration later today, hope that helps. Edit: It didn't help. It must be the battery.