Users report iPhones 6 and 6s turning off by themselves, cause not yet identified
Apple reps have allegedly said that the issue is known, but is still hard to pinpoint and reproduce, so a fix may take a while to arrive. Meanwhile, earnest users are trying to figure it out, and current theories suggest that the issue may be caused by corrupted iCloud backups. Interestingly, iOS 9.0.2 came right after Apple fixed some iCloud bugs that prevented developers from taking advantage of the new App Thinning.
The suggested solutions are two – reset all your settings (Settings -> General -> Reset -> Reset All Settings) and use the phone for a while in this manner. If it doesn't help, take the more drastic measure – factory reset the iPhone and choose "Set up as new iPhone". The latter is a pain, especially for those who have tons of apps. If you have any kind of iTunes backup that is semi-recent, you can try backing up from it, then filling out the blanks yourself. Otherwise, you will have to write down all the apps you currently use in a list, and restore them manually after setting up the iPhone as a new device.
Alternatively, if this issue isn't bothering you too much, you may want to wait a couple of days and see if Apple will announce that it is on it, or even fix it.
Thanks for the tip, Edas!