Legal Question in Business Law in California

No, you should appoint more directors, even your wife and children.

Wife and children? Minors are ineligible to be corporate directors.

Directors remain in office until their terms end and their successors are duly elected, or until they resign or are removed for cause. Therefore, if you once had a full board and the only reason for vacancies is failure to elect new directors upon the expiration of terms of the old directors, the old directors are legally still directors and you may have a full board but not know it. See Corporations Code section 301(b). This leaves open the question of whether you have a quorum. Refer to your bylaws for what constitutes a quorum. Without a quorum, the corporation may be unable to take actions requiring board approval - see Corporations Code sections 307(a)(7) and (8).

The foregoing is based on general corporate law. In most cases, the same rules apply to non-profit corporations, but there are some exceptions. Without knowing what kind of non-profit this is, e.g. public benefit, mutual benefit, religious, etc., I could not research more specifically.

Having a quorum present is the key to taking action at the board level. Keep in mind that corporations can continue to function as to routine matters without board action.