Mine actually fully reboots.
In the middle of the night usually.
I see the apple logo and then it turns back on.
Many others have experienced the same on stock is so not sure if Apple fixed this issue with the latest iOS release. Hope they did.
my 5s (9.0.2, jb) restarts every other 3 or so days, always overnight. really weird.
From what I gathered, it seemed to have been an issue with stock iOS when you enable DND mode while on the charger
Although that may not be true, I assumed it was a stock iOS issue since there were reports of others experience the nightly reboots on stock iOS devices too