Guillotine: Action cards on the field
I understand the confusion because the rules don't explicitly say it but logically:

You should also keep all action cards that are in the play area because they effect the points at the end of the game. If you discard them each end of day, then they are worthless in the first two days of the game. And that ruins a large part of the game.



I suppose you could play in a way where the action cards that effect points only affect the day they were played, so that you add up your points each day before discarding them. That could be an interesting variation but that is obviously not the original game because the rules do state that action card points are added at the end of the game:


  When the third day is over, each player counts up the points on his or her noble cards...and any action cards that might add to or subtract from the point total.


Since it never says to add up the action card points before that, then we must assume they are held on to until the end of game.