Vice Presidential Nominations are awarded by the Admissions office at the respective academies. The office of the VP send each academy a list of those who applied.
Only one can be admitted per year, per academy. If the nomination is awarded and the candidate chooses not to attend - the academy can nominate another candidate.
I only recall one candidate on this forum who received it over the past 4 years. Roughly, she applied to three academies, got three LOA's and One nomination to one academy. Her MOC would not consider her for other nominations and she received notification of her VP nomination from the academy and it was closely followed by an appointment.