The Server.Close invocation causes the connections towards the Proxy Adapter on Lightstreamer Server to be closed.
This causes Lightstreamer Server to fail, unless the "robust version" of the Proxy Adapter is used.
Hence, it must be restarted to go on; however, it should have logged something before closing.

It's not clear to us what you mean by "subscriber and publisher connection".
Moreover, I can't identify the client.CloseConnection method.
Do you refer to some connection that is managed by your Remote Data Adapter to get data from some backend process?
In this case, consider that the Server.Close method does not invoke any close method on the Remote Data Adapter. Hence, any housekeeping should be requested to the Remote Data Adapter by direct invocation.