Standing rules are to make user's comments bannable if their comments are systematically and significantly downvoted, and the user keeps making a whole lot of the kind of comments that get downvoted. In that case, after giving a notice to the user, a moderator can start banning future comments of the kind that clearly would be downvoted, or that did get downvoted, primarily to prevent development of discussions around those comments (that would incite further downvoted comments from the user).

So far, this rule was only applied to crackpot-like characters that got something like minus 300 points within a month and generated ugly discussions. private_messaging is not within that cluster, and it's still possible that he'll either go away or calm down in the future (e.g. stop making controversial statements without arguments, which is the kind of thing that gets downvoted).