My friend thinks that you can drop and then pick up the Brainstone as many times as you want in order to basically cycle through the deck to find the best cards. That seems like a really broken interaction. I think that the rules of the card prohibit this, but he says that the "first time" only applies to when it's cast, not when you pick it up.

Picking up items drains an action, so, you can't actually farm your whole deck in one round.

In any case, the card reads "the first time you cast or acquire " so in any case I'd say it works only for the first time (even if it's difficult to keep into account how many times you did this in the game). Regardless of whether my reading is correct, I'd suggest your friend to play the game so that all the players have fun, so, without trying to lawyering the cards to skew them in his favor. Had the sense of the card been coincident with your friend's reading, then the wording would have been really different

"the first time" is aka "once per turn" in card game, only change the time when it lasts, but it means only one time per turn