I can only think of three reasons why I might ban someone from playing in a tournament (as in, “you can never play in one of my tournaments again”).
(1) I have reason to believe that the safety of any player or tournament staff member is at risk.
(2) The player is not allowed at the venue due to prior decision of the organizer or venue owner.
(3) A player’s repeated misconduct was so egregious that it deserves permanent expulsion from my events.
I have seen cases in (1) and (2) before. Allen Priest’s example of (1) is more direct than mine.
(1) - I was helping to coach my high school alma mater’s team at a local scholastic tournament. Player A was a known behavior issue, who was fully enabled by his overbearing father. Player B was just another local kid. I didn’t have any connection to either of them. The two players were playing on Player B’s equipment, when a brief dispute ensued. Player A then purposely spit all over Player B’s board and pieces. Player B, naturally, didn’t want to continue the game. The TD threw Player A out, and his father appealed the decision. The TD put together a three-person appeals committee, including me. We took about sixty seconds to uphold his decision, and the Metro St. Louis Interscholastic Chess League wound up permanently banning Player A from any of its tournaments.
(2) - Player H had been previously banned from using the facilities of the Pittsburgh Chess Club. This ban was still in effect when I started regularly directing their tournaments in 2003, but I didn’t know about it. Player H showed up, wanting to register for a tournament. He needed to renew his USCF, so I took payment for that, and was about to take his entry fee when a club officer came up and told me that Player H was actually not allowed on the premises. I advised Player H of this, and he didn’t argue. I gave him his entry fee and USCF money back, and asked him to leave, which he did.
I would think that, to demonstrate (3), you’d want to have a pretty good paper trail. This should include, at a minimum: notes of any conversations you had with the offender, including date and time; full description of each incident, with witnesses if possible; and at least one warning by formal written communication advising the offender that he is risking permanent expulsion from your or your organization’s tournaments (sent via registered mail).