How about the shift happens at midnight, regardless if the PCs are sleeping or not, but if you make a high DC concentration check you can force the shift to delay for a certain number of hours. You can keep making concentration checks to keep delaying the shift, but it gets harder each time. Only one PC needs to pass the check, and other PCs can help using the "aid another" action.
I suggest that every time a PC attempts to stay conscious for the event, he must make a DC 50 Will save or fall unconscious for an apparently infintesimal amount of time. Eventually, someone will succeed by rolling a 20.
He who passes the will save is subjected to travel through raw time, something which mortal minds were not meant to survive. The local inhabitants (who also shift back and forth) advise to not fight it because everyone who has suffered horribly. (This will tempt the hell out of the PCs to fight the change, wink wink.) So the PC who stayed conscious is driven mad, but does gain understanding of either 1) why the time change is happening, 2) who is affecting the change, 3) how to stop the time change, or 4) the name and whereabouts of someone who does know these things.
So the PCs have to go around searching for a cure to the unfortunate PC's insanity, which is completely debilitating and uncurable except by a
Heal spell administered while the PC is the subject of a
Temporal Stasis spell. That will be hard to figure out and hard to accomplish, so you'll have a few sessions of adventuring after a PC stays awake and becomes insane before he's cured.
Once he's cured, he can tell everyone what he knows, one of those 4 things, which will help the party fix the problem and stop the time-changing from happening. Yay.