Actually there are no states that require AOA membership as part of the licensure process or licensure renewal process. Some states specifically require AOA Category 1A credits for renewal, but you don't need to be an AOA member to obtain those credits.
NOW if you are board certified through the AOA, then you must maintain membership in the AOA (be a member in good standing) as a condition for maintaining board certification. If you are no longer a member, then you are no longer board certified (by the AOA)
If you are board certified through one of the ABMS Boards, then membership in the parent organization (ACP, AAP, ACS, ACEP, etc) is not required. Nor is membership in the AOA required.