I believe its a one time use and its gone. If it doesn't get used, it can be sold for the gold value on the card at the end of the scenario.
This is partially incorrect because it implies that you don't get the gold if you use the card. That is incorrect; heroes add the gold value to their bank regardless of whether a search card is used or not.
To the OP: you really wouldn't want to house rule that heroes keep items between quests. There are only twelve cards in the search deck, and if you did not replenish it, you would very quickly run out of search cards.
I suppose you could house rule that cards get returned to the deck when they are used, but it still brings up the possibility of not having enough cards in the deck to cover all of the search tokens in a given quest, or even worse, if the heroes held all ten of the usable items, they would guarantee the Treasure Chest (which is immediately discarded) after only two searches, every quest.