Use of an access node's secondary-node-addition-failure history as a basis to control whether a UE will connect with the access node

A method and system for controlling whether a user equipment device (UE) that is not connected with an access node will connect with the access node. An example method includes making a determination of whether the access node has experienced a threshold high extent of secondary-node-addition failures, each secondary-node addition failure being an instance where the access node attempted secondary-node-addition for dual-connectivity service and the attempted secondary-node-addition failed. And the example method includes using the determination as a basis to control whether the UE that is not connected with the access node will connect with the access node. Without limitation, this example method could be carried out by the UE when the UE is seeking to acquire initial wireless connectivity or considering handover to the access node, or the method could be carried out by a source access node considering handover of the UE to the access node.