I agree with the other posting attorneys. What is going on here is that you do still have mail service, just not the convenient mail service you expected. That is why you then need to look at your CC&Rs to see what obligations have been expressly set out for the Association to provide mail receptacles. If there is language, you would then be looking at recovering your expenses from a breach of contract approach (which is fairly important since it would likely also include recovery of attorney's fees if you had to get one involved). If not, then you will know that you likely have more of an issue of pushing your Association politically by banding together with your other owners to demand the replacement of the mailboxes and the payment of expenses for getting the mail at the main post office.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. I am licensed in Arizona and can only provide general comments on matters outside of Arizona law. Actual legal advice can only be provided after a direct consultation in which all of the relevant facts are considered before providing a response.
You have mail service. You can pick up your mail at the post office. If you have expenses in doing so, you can ask the manager to reimburse you. Maintain photos and keep all evidence in case you need to sue them in small claims court.
You also want to review your CC&Rs to see how to properly file a complaint and the remedies that are available to the homeowners.
Please note that I am answering this question as a service through Avvo but not as your attorney and no attorney-client relationship is established by this posting. An attorney-client relationship can only be established through signing a Fee Agreement and paying the necessary advanced fees.