A technique prevents multiple multicast forwarders from forwarding multicast packets for a route over a link in a computer network during non-stop forwarding (NSF) recovery of one or more failures in a control plane of a multicast router. The multicast router has a functional infrastructure that allows data traffic forwarding operations to continue throughout a data plane of the router in the presence of a failure and/or software restart to a multicast component, e.g., a protocol independent multicast (PIM) routing protocol, executing in the control plane. Another multicast component, e.g., a multicast forwarding information base (MFIB) executing in the data plane, is configured to prevent multiple multicast forwarders due to routing changes in the network that arise during NSF recovery.