So it only reboots when idle or in deep sleep and not connected to a power source. My first thought is that this is a hardware fault, but an unusual one. Has it just started or has it always been like this? And are there any other factors, e.g. it only happens after the battery level has dropped below a certain point?
My first thought was that maybe it was related to the regulation of the SoC core voltage vs clock frequency? The phone's processor will adjust the voltages within it according to the clock speed in order to save power, but if you set them too low it will crash. When that crash would occur would depend on which bit of the voltage vs frequency table was too low for some part of the chip: in this case, if it's crashing when sleeping, that would suggest that it was the voltage for the lowest clock frequency that was the problem. Of course the manufacturers set the thresholds so that any chip that's within specification should be able to cope with them, but the chips do vary and there may be the occasional outlier. That's why I asked if it's always been like that: I'd think this is more likely as a result of manufacturing tolerances in the chip than wear or damage, though I don't know enough to rule that out.
The other thing is that not crashing when charging might suggest that the battery isn't supplying sufficient current or a high enough voltage. But if that's where the problem lies you'd expect it to happen when the phone was in use, and so making the greatest demands, rather than when it's been in standby for a few minutes.
In any case, while it's really hard to give a definite diagnosis online, I'm afraid that my instinct here is that this is a hardware issue.
