An idea stolen outright from X-Files, with a dash of "Before and After"
Title: Sleep, Perchance to Dream
Era: Any
Setting: Any
Perhaps best as a solo episode where you can run the other normal players as NPCs, say one night where not enough people show up... Exposed to a field via sabotage, one of your crew loses consciousness, and wakes up X days later. Everyone else seems to think it has been business as normal, and routine medical scans show that there is memory loss alright, but no real permanent damage seems to have happened.
It's unfortunate, though, because the crewman affected learned something valuable shortly after the act of sabotage, and the intelligence agent that was on board working with him has just been killed, and under Starfleet Regs, the crewman hadn't told anyone else who the saboteur was - because the agent was undercover, and there was a sting going on to find out the bigger picture about the saboteur and who was supplying him/her.
So: day 1 has the crewman being found with the dead agent, and likely framed for it, investigation long into the day, and being tossed in the brig. But whe he wakes up... it's the day before this, and he wakes up in his quarters...
Moving backwards, the intelligence agent is killed again, until the crewman figures out that (a) it's an intelligence agent, and (b) the crewman has been working with him to figure out who did the sabotage. From the backwards information, the crewman, each day, will get a little closer to uncovering the act of sabotage, and who the saboteur is, and then, waking up the day of the actual incident, stopping it from happening in the first place, which ends the cycle, and leaves only him the wiser, the agent with his man, and the saboteur in gaol with the greater organization exposed.
The Doc