You're not the
first person to ask this, although the answer isn't 100% certain yet.
My theory is that it would indeed switch between both players on their respective turns. The same would go for a Thief that stole the
Boomdagger from a different Thief and then discarded it for a Theft attempt of a different Item.
Also note that it is quite difficult for a Cleric to get the
Boomdagger out of the discard pile anyway. He can only use Resurrection when he would be drawing face-up cards, with the only reliable way of doing so with Treasure being to win a battle with a helper, and you can only take a helper if you are losing a battle.