You raise my favorite question for nonprofit organizations: Whose organization is it?  (See Ready Reference Page: “The Key Question: Whose Organization Is It?”)

Federal rules for 501(c)(3) organizations do not establish criteria for governance issues such as this.  The IRS generally does not care who controls the organization so long as it operates “exclusively” for charitable purposes.

State law governs the governance question and generally divides corporations between membership organizations, where members have voting rights analogous to shareholders of a business corporation, and board-only corporations.  The organization and its members (if there are any), get to choose. Your group apparently chose to have the board self-perpetuate and treat the “members” as contributors or supporters rather than as voting stakeholders.  Whether or not there should be voting members, in my view, depends primarily on the answer to my favorite question and whether the “members” would be sufficiently interested in the activities of the organization to pay attention to its governance.  The board can always amend the bylaws again to invest members with voting power, but it is pretty hard to get human beings to voluntarily give up power.