Sounds like you've got a security problem at your hospital!
Anyway, a properly designed ESU shouldn't fail just because the cable was yanked (or whatever).
And a decent power supply should be able to withstand "voltage transients", as well.
Meanwhile, I'm trying not to waste too many (of my diminishing) brain cells trying to imagine how any "internal log" could decide that a piece of kit was being switched on and off at the wall! Maybe just a few missing front panel PWR_DOWN* signals from the log, but surely the unit wouldn't power up just by flicking the wall switch on (that is, only the front panel button - PWR_UP? - would do that)?
I'm calling BS on all that.
But here's a thought - how about a dodgy (sticky) front panel on/off button, or "bad" connections to same?
* I'm just guessing with that one - but I expect it's something similar.