Cannot shutdown a shutdown connection MySQL Enterprise Monitor
There is really nothing you can do once a shutdown starts. Why ?

According to the MySQL Documentation on the Shutdown Process


  2 The server creates a shutdown thread if necessary.
  
  Depending on how shutdown was initiated, the server might create a
  thread to handle the shutdown process. If shutdown was requested by a
  client, a shutdown thread is created. If shutdown is the result of
  receiving a SIGTERM signal, the signal thread might handle shutdown
  itself, or it might create a separate thread to do so. If the server
  tries to create a shutdown thread and cannot (for example, if memory
  is exhausted), it issues a diagnostic message that appears in the
  error log:

Error: Can't create thread to kill server

  
  3 The server stops accepting new connections.
  
  To prevent new activity from being initiated during shutdown, the
  server stops accepting new client connections by closing the handlers
  for the network interfaces to which it normally listens for
  connections: the TCP/IP port, the Unix socket file, the Windows named
  pipe, and shared memory on Windows.


It sounds like you are past Stage 3 because you got Connection refused: connect

In addition, note what may have triggered Stage 2:


  If shutdown is the result of receiving a SIGTERM signal, the signal thread might handle shutdown itself, or it might create a separate thread to do so.


What could be that trigger ? Stage 1 says regarding Windows


  A server running as a service on Windows shuts down when the services manager tells it to.


At this point, you have most likely reached Stage 4, which would go on to terminate currently active connections.

CONCLUSION

Maybe a Bug Report or Trouble Ticket would be in order. Just make sure you have done your due diligence in terms of finding out if the Service Manager died or that human error or lack of memory on the Windows box was ruled out.