If your HOA is incorporated, then the law requires that article of agreement be on file with the New Hampshire Secretary of State. Use this site to confirm (or deny) that your HOA is incorporated:
https://quickstart.sos.nh.gov/online/BusinessInquire
Then contact the Secretary of State's staff and ask how you can get a copy of the Articles of Agreement.
Regarding the number of directors falling below what you say the bylaws require:
I hear you that a bylaw violation is likely in place.
To enforce bylaws, court is an option. How would a court handle this? I could see an exchange going like this in a courtroom:
Owner X:
Your honor, the Bylaws require five directors. I want the court to force owners to serve.
HOA attorney:
Your Honor, no one else will serve. I do not believe the law can require an owner to be on the board against his or her will. The HOA's governing documents are clear that board service is a volunteer duty.
Judge:
I agree. Owner X, my hands are tied. But what about you? Will you serve on the board?
Owner X:
Your honor I am too busy with family and work to serve on the board.
Judge:
[The judge nods in acknowledgment. Then the judge wonders about receivership.]
I understand. But let me ask: Is there imminent harm to the HOA by having only three (or even two) directors? I know the Bylaws are being violated, but I also want to do what is best for the HOA. Sometimes a court can ignore bylaw violations. It just depends.
Owner X:
I think ___ and ___ represent imminent harm.
HOA attorney:
Your honor, the current board of three (or two) is addressing these issues, as evidenced by these receipts for payment for [such-and-such] services and these board minutes.
Judge:
Owner X, I just want to make sure you understand a few things. First, receivership is highly expensive. Are you okay with paying more in monthly dues so that a receiver runs the HOA?
If so, then second, I want to know whether you believe one head (a receiver's) is really better than the two or three heads currently serving as directors.
The judge rules on whether this alleged imminent harm justifies going into receivership.
So far I personally do not think there is enough evidence of imminent harm to justify a court appointment of a receiver.
In my experience the courts very much prefer people work out their own problems, if at all possible. Sometimes it is not. But here, and so far, I think the HOA is better off with only two directors compared to having a receiver, even if this is a violation of the bylaws.
I hear your frustration. I am working with another organization that relies exclusively on volunteers from its roughly 150-person membership. This organization is s under the umbrella of a nonprofit corporation. Maybe 10 percent of the membership does the work. It is a massive, thankless amount of work. The members become acclimated to others doing all the work for them.
What I have learned over decades is to never expect people to step up. Still I often explain to members that if they have complaints, they should step up and volunteer for such-and-such role. They do not. It says a lot about human nature (or maybe people's values) today. It is a greedy world. My hat is off to all of you serving on HOA/COA Boards.