What happens when nonprofit officer moves away?

It sounds like you are asking two questions here.  Should the person remain in office as Vice President, and should the person remain on the Board as a director?  Unless you have some unusual provisions in your corporate bylaws requiring either officers or directors to live locally, there is no general federal tax law or general state law that I am aware of that requires termination from either position.  The choice will be up to the individual and the organization.

A Vice President, whose required role in the organization is to substitute for the President when the President is not available, may have more difficulty in filling in for Board meetings or other ceremonies while living in another state. If you treat the Vice Presidency as a training ground for the individual to succeed the current President after a few years, you may want to remove the individual from the office and groom someone else.  If the individual doesn’t want to resign, you probably have the right to remove the VP from office if your Board simply thinks it is in the best interest of the corporation, without having to prove legal “cause.”  If the person’s living away won’t disrupt your expectations, particularly if the person is filling a position that no one else wants, you may be happy to leave things as they are until you can recruit someone willing and able to succeed to President.

The Board position is a little different.  There is very little that a Director can’t do from away.  If the individual provides a diversity of view or experience that you think is valuable for the organization, there is no doubt that they can still contribute vigorously to Board or committee meetings by Zoom or other electronic means.  National and international nonprofits regularly include directors who are not local, but are critical to the organization because of their knowledge, their reputation, their advocacy (and occasionally their money).  If your bylaws permit removal of a director only for “cause,” failure to attend meetings in person is probably not cause because most state statutes say that attending by electronic means is deemed to be attending in person.

Assuming that the person would like to continue on the Board, and that the person was elected to the Board in the first place for good reason, there would seem to be no reason to ask the person to leave the Board merely because they moved away.  If they were a good Board member last month, there is no reason to assume that they won’t be a good Board member next month.  If it doesn’t work well, you can always decide not to elect them for another term.  But if you have someone who has been helpful in the past, it would not make sense to me to automatically cut that help off from the future.