Off the shelf, a Kanban board's "done" column works off a "release". If an issue has a fix version, then it will not appear on the board, because the board sees the version as the "release". You clear out the column by using the "release" at the top of the column, which sets the version to something when you use it.
You could do it slightly differently - change the board filter so that it includes a clause like "and not (status in (<status in your done column>) and updated < -28d)". That will drop older done issues off the board automatically.
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