At any time before or during the review proceeding pursuant to Section 61-1-17 N.M. Stat. Ann., the aggrieved party may apply to the board or file a motion in accordance with the Rules of Civil Procedure for the District Courts in the reviewing court for an order staying the operation of the board decision pending the outcome of the review. The board or court may grant or deny the stay in its discretion. No order granting or denying a stay shall be reviewable.