The board shall meet once each month at a time and place to be designated by the board. Special meetings may be held as often as the needs of the district require on notice to each member of the board. A majority of the board shall constitute a quorum at any meeting. Any vacancy on a board elected by qualified electors of the district shall be filled by the remaining members or member of the board, the appointee to act until the next biennial election when the vacancy shall be filled by election. Any vacancy on a board appointed by a board of county commissioners shall be filled in the same manner as original appointments, in accordance with Section 73-21-15.1 N.M. Stat. Ann., the appointee to act until the end of the term of the member creating the vacancy. If the board or a board of county commissioners fails to fill any vacancy within thirty days after it occurs, the court having jurisdiction shall fill the vacancy.