what i've surmised is that some checks will never work no matter how high your persuasion is. the thing you want to pay the least attention to is the stat associated with the check; i've failed intelligence checks but succeeded on wits checks with high int mages that i've put at most one extra wits point into. the game seems to put more emphasis on the actual message your character says with each check - does it seem like this would reasonably persuade anyone? if the answer is no, it's unlikely that even high persuasion will do it for you
there definitely seems to be certain persuasion options in each check that absolutely will not succeed no matter how high the stat or your persuasion level is. i always max persuasion in games like this, so when your persuasion is as high as it reasonably can be for where you are in the game and your check is still failing, it's probably indicating that that specific option is impossible
