OK, the power is off, your radio controlled (atomic) clock is now unregulated. Sooner or later the batteries in clocks, wrist watches, etc die. So how are you going to tell time?
I have two wind up clocks. An old Big Ben alarm clock that requires a wind every 24 hours and a wall clock with a 31 day movement. Neither is very accurate.
How important is real time in a scenario where the average zombie is only concerned with 'dinnertime'?