Search will stop functioning after this turn.

[ehunt]

I'm unclear why the log says this (I think when a second pile is empty). It's still the case tht Search gives +2 after this turn, and that any searches in play get trashed at game end (which might matter for various Alt VP conditions).

[Ingix]

The line means a Search that was removed from play this turn will stop functioning later. It isn't talking about other Searches played afterwards.

If it left play due to a pile becoming empty, than the line is not saying anything you didn't know before. It shouldn't really be there in that case. If Search left play for some other reason (usually with something like Way of the Horse when played using a Throne Room), the line reminds you it will no longer have its normal effect on later turns.