The error is shown as a pop-up dialog saying, "PuTTY Fatal Error: Server unexpectedly closed network connection". This happens more often when the connection goes through a proxy server.
To void the error or the disconnection, you can set up the PuTTY Connection to send NULL packets to the server at a specified interval. In the example shown, PuTTY will send a NULL packet every 10 seconds. With this, connection session will be kept alive until you close it.
However, be aware that this setup makes your machine vulnerable. Please remember to CLOSE the CONNECTION when you don't need it!