Any member of the Board who fails to attend three consecutive meetings of the Board shall be considered automatically removed and a vacancy shall be deemed to have occurred unless a showing of good cause is presented to the City Council. The City Council shall be the sole judge as to whether or not good cause is shown. If a vacancy shall occur other than by expiration of a term, it shall be filled by appointment by the Mayor with the approval of a majority of the City Council for the unexpired portion of the term. Nothing in this chapter shall preclude the City Council from reappointing members to the Design Review Board.