This is a question of state law and may depend on whether or not you have a membership organization where members other than those on the board have the right to elect or remove directors.  If members have the power to elect or remove directors, it is unlikely that you can prevent them from making changes to the board, and certainly not if they object to bylaws trying to take away their power.

If you have only a self-perpetuating board and no voting members, it may be possible to draft bylaws that allow all of the founders to serve for life without anyone else on the board, but I don’t think would be a very good idea.  I don’t believe in term limits for directors.  (See Ready Reference Page: “Term Limits Are For Cowards”)  And I do believe that founders should protect themselves so that they can continue to pursue their mission if others on the board want to take a different direction.  (See Ready Reference Page: “Sole Member Bylaws Can Protect Founder of Nonprofit”)  But in each of these situations, we contemplate additional board members who continually bring new ideas and new vigor to the organization.

If only the founders can ever serve, you give up on the influx of new ideas. You don’t have any way to deal with your own internal divisions or the drag of a permanent dissenter who keeps you from focusing on your objectives.  You couldn’t even replace those who die, move away, or simply drop out for lack of interest.  If everyone has been there forever, you all know why things can’t be done.  But newcomers with a different perspective and a different energy level might actually accomplish what you “know” can’t happen.

Maintaining the vibrancy of the board is one of the main tasks of any organization.  It doesn’t require expensive elections and is not an unnecessary activity irrelevant to your success.  It is really fundamental to completing the objectives of the nonprofit successfully.