This sentence is not giving you an option to stop playing the card set aside with Prince, it is telling you a circumstance under which Prince stops "working" (that means it no longer plays the set aside card each turn). It's (in 99.9% of cases) a disadvantage.
The easiest example are Duration cards; they are (usually) not discarded at the end of the turn they are played, so Prince fails to set them aside and so, by the sentence you gave, will not play them any more in future turns.
Other examples are cards that can trash themselves, like Mining Village, or that move themselves elswhere (say to the Supply with Way of the Butterfly).
