If no members run for an office during an officer election, can two offices be combined without amending our bylaws? (Recording secretary, and corresponding secretary). Or should one office remain open and unfilled?
You probably have a middle way. Check your bylaws (or state nonprofit corporation law) to see whether the Board has the authority to fill a vacancy among the officers. It normally has that power. If so, the Board can either ask the member who was elected to one of the positions if they would be willing to serve in both positions or appoint another member to the vacant post. I am not aware of any law that prohibits a person from holding more than one secretarial office at the same time, although some bylaws prohibit the same person from holding more than one position in certain situations, such as not being president and treasurer at the same time in order to provide an internal check and balance on the funds.
If you think this will be a chronic problem for your nonprofit, you can amend the bylaws later to have a single secretarial position.