Persuasion doesn't always clamp the resulting disposition
Although console command getdisposition won't record a number lower than 0, NPC disposition can go negative without limit. For example, being caught stealing an item can set an NPC's disposition to -100 or lower. Successful persuasion attempts will appear to have no effect, as the persuasion bar doesn't show values lower than 0. It can take a great number of successful persuasion attempts to visibly raise it above 0.
Vanilla appears to cap minimum disposition at or near zero. No more than two successful persuasion attempts are necessary to bring it above 0, even if console is used to set disposition to -100.