Multi-turn debuffs?

A good example would be Palps stun for 2 turns ability. Does anybody know if the debuff lands on a character, is there a chance that debuffed character can resist the stun on the 2nd turn? Or is it automatically going to stick regardless of tenacity. I ask because while battling through the ocean of Palp leads in arena, it seems like sometimes my characters become cleansed quicker after being stunned from opponent to opponent. It's hard to tell because of how fast things move sometimes, if 2 turns had passed or my character shook the 2nd stun.