PaulS:
If there are a limited number of connections (like the Ethernet shield can only handle 4 simultaneous connections), and you use one of them for a telnet session, so that you can be told twice a day that the door opened or closed, then that connection is not available for any other use. Hence it is tied up.
It that one connection is nothing, this implies, to me, at least, that it isn't 1 of 4. Rather, it is one of so many that one doesn't matter.
So, which is it? Are you tying up one of a limited number of connections, where it could matter, or one of so many that it doesn't matter?
I do nothing, I only recommend using the simplest way.
esp8266 can handle 5 sockets. This project needs one socket on the client esp8266. On the server one socket is the listening socket a second socket is the current client. server side sketch can refuse more clients by simple stopping the incoming connection.
the OP can decide if he lets the client connection alive or closes it after every event. if the client closes the connection, the server side closes it too. I would close the sockets after the event in this case.