Laverne,
The duties of the VP is typically to fulfill the duties of the President when the President is not available.
FL 617.0840 requires such Officers as are named in your articles of incorporation. In order to comply with the statute, the Association should have those officers. Typically, these include the President, VP, Secretary and Treasurer.
Additionally, your governing documents may limit the number of Officer positions an individual may hold at one time.
If your VP doesn't want to perform the duties of President or is only willing to perform them until one is assigned, it appears that you need to find someone as soon as possible to fill the vacant seat or reassign the current officer positions so you are in compliance with applicable law and your governing documents.
To me, expecting that you meet monthly, as soon as possible would be within 3 month (can be sooner and, if possible should be within 2 months).
Month 1 - Resignation announced
Month 2 - Solicitations for someone to fill the position
Month 3 - Board votes to fill position based on responses (or lack of responses)