This is an interesting question that I haven’t had raised in my practice.  Assuming that there is nothing in your state’s nonprofit corporation law or your bylaws on the topic, I think you can decide whether you want to permit it or not.  For guidance, I would suggest that you look at Rule 14.a-8 of the Securities and Exchange Commission on shareholder proposals for publicly traded companies.  The rule and its commentators have probably done the most comprehensive thinking on the issue.

The SEC rule requires a certain amount of ownership (you may want a certain number of members) who have owned the stock (been members) for a certain period of time.  They require a written statement of what the shareholder (member) wants to present to the shareholders (members).  They require the shareholder (member) or appropriate representative to attend the meeting to discuss the proposal. They require the request be submitted a certain period of time before the meeting and that the shareholder be available to meet with the management before the issue is included in the proxy request.

The rule also lists 13 classifications of proxy votes that can be excluded entirely, including those that request action that would be illegal or improper, that the organization would not have power to implement, that express a personal grievance that would not be relevant to most shareholders (members), that has already been substantially implemented by the company, and that would be duplicative of questions previously submitted.

Depending on your predilection for corporate democracy, the Board may decide it is a good idea and support member proxy questions, but I think it would be important to develop standards if you intend to do so.  The Board might also think it is a bad idea and prohibit it.   In either case, the members can ultimately decide, and vote out a Board that doesn’t agree with them.