The permissions analyser would only give you a view of the user's capabilities based on what actual permissions he has. As such, as banning isn't technically a change of permissions, this usually wouldn't be an accurate reflection.
If he is able to bypass the reply ban, and you're certain he should be banned, I do wonder whether there's an add-on at play here. If an add-on has made a bad job of extending the method that checks whether a user can reply or not then it's possible the reply ban check is being skipped.
First, see if you can reproduce the issue on a test account. If you can, then it will be easier to test. The test would unfortunately just involve disabling all add-ons and trying again on the test account.