I'm also pretty sure what you actually say affects the outcome a lot. Is the character you try to persuad a proud warrior? Probably a bad idea to belittle his strength/honor, no matter how high your stat is for that answer.
I've won persuasion a check with 0 persuasion in act 2 once. Also won a lot of checks picking stat answers that my character doesn't even take (like finess on a int character), although that was an a 4+ persuasion character.
EDIT: Excatly what miaasma said.
a better way to go about using persuasion is to look at who you're talking to and figure out if the persuasion option, dialogue-wise, looks feasible. str options tend to involve intimidation, but if you are trying to intimidate an ogre or a confident warrior, you are likely to fail
this is because the game writes persuasion into the game rather than making it a flat stat check you can pass or fail; some checks will be literally impossible, while others will be passable with zero levels in persuasion