Update: The problem cured itself. I went away for a half-hour, left it plugged in, and came back, and it was booted up but not rebooting. First thing I did was initiate a backup. :-)
I'm having a problem with my iPhone 6s-plus.
1. I let the battery run down to empty.
2. Plugged it in to charge it up.
3. Wait a minute.
4. It starts up.
4. It shuts down.
5. Go to 4.
I left it alone for a half-hour and it's still doing it.
What do do?
To help rule out a software problem, try resetting your device. (While it's plugged into the charger, hold down the Sleep/Wake and Home buttons for 10 seconds or so until the Apple logo appears.)
Thanks. Not sure how I could do that because the phone reboots immediately on booting. (Update: It cured itself. See the note at the top of this post.)
Your situation could obviously be different, but when My iPhone 6 did something similar it was because the charge cord wasn't connecting properly. It wasn't really charging. When my high-tech attempts to diagnose the problem failed, my wife pointed out the obvious. My phone's charging jack had lint in it. After a lintectomy with a toothpick, it started charging a booted immediately.
This was with two different cords, two different computers it was plugged into.