No, your RAD registration is perpetual so long as the ownership does not change. If your initially own the property as an individual but later decide to move the property to a Trust or Business Entity that would be conisdered an ownership change which would require a new registration (and new basic business license and Certificate of Occupancy, if applicable).
However, you must maintain your registration. If a housing accommodation or rental unit, initially exempt from rent stabilization, becomes subject to rent stabilization later on, the housing provider must update the RAD Registration or Claim of Exemption form accordingly. Any alterations in ownership or management must be reported to RAD within 30 days of the occurrence. Unregistered housing accommodations or rental units are automatically subjected to rent stabilization until the property is registered with an approved exemption.