Hi Andrzej,
Thanks for your question. This falls under the loop rules (specifically, 719.3):
719.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.
In short: the active player will have to choose a number of times to activate, then the nonactive player (knowing that number) can activate it more times, and then we're done (the active player is not allowed to activate it anymore). In this case, the active player (the one casting the Protection) will have to stop before their opponent does.
Thanks,
Nathan Long
Magic Rules NetRep