At the discretion of the appointing power or body, a member of the commission may be reappointed or may continue to serve if he or she no longer continues to function in the capacity which originally qualified him or her for appointment. However, where Section 1799.2 requires that an appropriate organization submit names to the appointing power or body, a person shall not be reappointed pursuant to this section unless his or her name is submitted by that appropriate organization.