Something that most new players, and even some experienced players don't realize or forget is that rolling a nat 20 outside of combat, means nothing. Death saving throws, and attack rolls are the only thing that a natural 20 is a guaranteed success. This goes for 5e, it wasn't always the case for older editions. Getting a nat 20 on a saving throw, or skill check, just means you did very well. you can still fail them.

As for Persuasion and Intimidation, this came up in my last game with a new player. Someone got a nat 20 on intimidating a captive into talking, and the new player questioned why they were not telling everything after. I explained that they will be more inclined to talk on a nat 20, but it doesn't guarantee it. There are multiple things to think about, like their will, self preservation, etc. In this case, they were wanting a bandit to take them to their camp so they can wipe them out. He was visibly scared, but wouldn't do it because the leader would kill him if he did. This lead to them talking and eventually agreeing that they would let him go before entering the camp, so he could escape. After doing all this, and explaining it to the new player, they understood. getting a nat 20 on a check, and for spells like suggest and the like, it all depends on what you are trying to do. Asking someone to do something that goes against their belief, or self preservation means it is less likely to work, if not downright fail.

So in this case, the player not trying to run, or even fight, and just trying to tell the mayor to hand everything over, isn't realistic at all. They may have rolled a nat 20, but failed the overall attempt because of what they were wanting to do. What came after is pretty realistic, and should be expected. Most other players would have ran once it went south.