Professional society membership in and of itself is not completely necessary for board certification, right? For instance you could maintain the ABIM boards but not necessarily maintain membership in the ACP.
For ABMS and its member organizations (like ABIM, ABP, ABS, ABA, etc), initial board certification involves completion of residency (and/or fellowship) plus passing their test (some are written only, some are written + orals).
To maintain certification status, you have to enroll in their respective MOC program and do activities in the MOC to keep your certification active. (ie enroll in ABIM's MOC to maintain your IM certification, enroll in ABP's MOC to maintain your peds certification, etc)
You do not have to be a member of the ACP, or AAP in order to maintain board certification. Eligibility for college fellowship (not fellowship after residency, but an honor to be inducted as a fellow into a society/college) is not automatic after being board certified. There are certain criterias that must be met. If you qualify, apply, and are inducted into their fellowships, you may use FACP for ACP (for FAAP for AAP, or FACS for ACS), then you must remain a member in good standing in those organizations in order to continue to use those designations. *
In the AOA World, the AOA requires membership in the AOA as a condition for maintaining certification. So if you are AOA board certified, and you choose not to pay your dues, or you don't have enough AOA 1A CME credits (the AOA requires 150 hrs q3 years), then as soon as you are no longer a member of the AOA, you are no longer board certified.
The AOA is also doing something similar to the MOC programs that the ABMS are doing, except the AOA is calling it "OCC" (osteopathic continuous certification). Same hoops to jump through, still have to pay $$$, etc.