Is this message appearing in the initiator or target instance SQL log?
Are messages being sent, received and acknowledged or are they stuck in the transmissions queue?
Are you using the Availability Group Listener IP in your Service Broker Route?
Have you set the Service Broker route to use the Service Broker port (not 1433)?
Have conversation end points been opened?
Have you tried capturing extended event or profiler information (on initiator and target), capture all Service Broker events + broker related security/audit events to identify the point of dialog failure?
Is the endpoint stopped or disabled?
Sorry, there isn't enough information in your post to help much.