Susan,
Does your governing documents have the membership elect Officers as well as Directors?
It's not unheard of, but it is uncommon.
Keep in mind that Directors and Officers are two different positions/jobs in the Association.
It can be confusing, and many think that they are one position because most Associations have one individual filling both positions - Director and President as an example.
Regarding the Directors seat:
Expecting that your association is incorporated, most are but check to be sure,
TX Sec. 22.212 VACANCY of the corporate code applies when a directors seat is vacant. Typically, the remaining board members will/should appoint someone to fill the vacancy.
Regarding the officers seat:
Sec. 22.232. ELECTION OR APPOINTMENT OF OFFICERS defers to your governing documents - meaning that the procedure to fill an officer vacancy would have to be followed. However, if your governing documents are silent on how to fill a vacancy (vs. electing) then the statute specifies that the Board would/should appoint someone to fill the vacancy.
Until the vacancy is filled, the Vice-President would assume the responsibilities of the President.