I suppose that you are talking about a Remote Server based on the Java Remote Adapter SDK trying to connect to the Proxy Adapter on Lightstreamer Server.
It is possible that connection attempts are refused, because the Proxy Adapters only listen on their port when needed. After they receive a connection, they stop listening.
We should check the state of the listening port at the time of the issue on the Proxy Adapter log.
What versions of the Server and the ARI SDK are you using? This may affect the way the log is produced.