Patch deployment and client notification are two completely different things. Successful patching (or any other standard ConfigMgr activity/action) is meaningless when it comes to client notification. Also, client showing as "active" has nothing
to with client notification. Active simply means that the client has reported in to the MP recently (in the form hw inv, sw inv, heartbeat, or a policy request).
Client notification requires a persistent connection initiated by the client to the client's MP on port 10123 (or 80 as the client will fallback to 80 if 10123 if not available although this does cause more load on the MP).
However, the dialog you have above is not generated by ConfigMgr or client notification. It looks like it is being generated by one of the right-click tools which truly have nothing to do with ConfigMgr. For most of the tools to work, you must be able to
communicate from the console you are working on (since the console is calling the right-click tool) to the target system. Some right-click tools use psexec or WMI and some use WinRM. If the tool cannot make a connection on the appropriate protocol channel,
then it will give you the above message. Ultimately as mentioned though, this has nothing to do with ConfigMgr