To replicate: Get a Pokémon with False Swipe and one with Berserk. Make sure the False Swipe does > 50% HP to the Berserk mon (I boosted with Swords Dance). Hit the Berserk Pokémon, it will drop below 50% and activate Berserk as it should, but then every hit after will also activate it.
I think this is because the game is seeing that the move does > 50% and the Berserk Pokémon is still alive, and then concluding that it must have started with >50% HP so activating Berserk. If that's the case then this seems to be an interaction unique to False Swipe/Hold Back since any other move that does >50% to a Pokémon with <50% HP would kill it.