I recall reading a short story by Philip Jse Farmer wherein the crew of a spaceship land on a planet, go fumbling about in the mysterious alien ruins, and wake up the next day with no memory of the previous day’s events. Therefore, they go fumbling in the ruins again, and wake up… etc., until somehow they devise an ingenuous method (can’t remember what it was, but I’m sure it was ingenuous, or maybe just genius or Janis or Janus, who knows) to retain their knowledge and get the hell off of Dodge.
But of course I forget the title or in what collection or anthology I read it. I do remember Farmer relating in a preface that the story originally was a rejected script he submitted to the original Star Trek.
Other than the fact that they are forgetting more days every time they wake up, your description isn’t very close to the plot of the Farmer story. Farmer’s story is set on Earth. An alien spacecraft is circling the planet. Everyone in the world is losing their memories. Eventually they figure out a way to destroy the spacecraft.
You may have confused it with another Farmer story, The
Sliced-Crosswise Only-On-Tuesday World, in which, because of overpopulation, everyone has to spend six days a week in suspended animation and can only come out one day a week. Farmer later expanded the setting into two novels.