What next steps do we take if a nonprofit board does not meet for its annual meeting due to sickness and scheduling conflicts?
You don’t say who the “we” are who are concerned. If the “we” are directors of the corporation and simply talking to the leaders won’t get an annual meeting scheduled, certain of the officers individually and a small number of directors collectively normally have a right to call a special meeting of the board to conduct important business. If the “we” are voting members of the nonprofit, occasionally the members will have a right to call a special meeting of the board in addition to their right to call a special meeting of the members, but it may be a lot more difficult to get enough signatures to do so. Look at the bylaws and your state nonprofit corporation law to see who has the right to call a special meeting of the board, and if you do call a special meeting, how much notice you have to give to the directors and whether you have to spell out the business to be conducted at such a meeting. If the “we” are not people who can call a special meeting, you can only importune the people who can.
You normally don’t have to worry about adverse legal consequences from a failure to hold an annual meeting when scheduled, however. The most significant business of an annual meeting is normally to hold elections for officers and directors whose terms are expiring. State laws and bylaws normally say that the terms of officers and directors run for a certain period of time and “until their successors are elected and qualified.” The current officers and directors will continue in office, therefore, until the new elections are held, whenever that may be. The corporation can continue to act without a loss of its leadership. (I realize the reason you want to hold an annual meeting now may be to hasten the loss of certain of its leadership, but that may just have to wait.)
If you don’t hold your annual meeting on time, you will not be alone. It is not unusual for a nonprofit to miss its meeting schedule, for any number of reasons, some more legitimate than others. It may be annoying, but it is not likely to be disabling.