A board member should be asked to leave the board if they are not following the rules or are not coming to meetings.
Board members should understand all the rules, but the most important ones are the rules around conflict of interest and confidentiality. A board member who is clearly in conflict, but does not recuse themselves from a decision, should be given a warning. A second offense should lead to removal from the board.
Likewise, a board member who discloses confidential information should either be warned or removed from the board, depending on how serious the breach is.
A common situation which will lead to a board member being removed from the board is absenteeism. A board member cannot be effective if they are not at a meeting. A policy should exist which specifies the number of meetings that can be missed before leaving the board. This policy should be enforced all of the time.
Organizations are always in need of volunteers. Removing a volunteer can seem like a bad idea, but keeping people on the board who do not follow the rules is worse.