It depends on the type of membership that you join.  If you are a Professional, Young Professional, Global eMember, Collegiate or Associate member, the membership is yours and goes with you if leave an organization.
The Nonprofit Organizational Membership for both large and small organizations, and the Executive Circle Business Member or Endorser Business Member belongs to the organization or company.  If an employee leaves, the organization may replace the name of the designated member.  New members still need to fill out a membership application and sign their adherence to the AFP Code of Ethical Principles and Standards.