Windows Remote Desktop: The terminal server has exceeded maximum number of allowed connection, mstsc

I kept getting the dreaded 'The terminal server has exceeded maximum number of allowed connection' when attempting to log onto a remote server. I must've forgotten to log out and just clicked close on the mstsc session!

The answer:

You can start a control session to the server and logoff your other connections. Please always use "LogOff" when you leave remote desktop.

Open Command Prompt.
Type: "mstsc /admin".
Remote Desktop Connection will start. Type the computer name or IP address of the computer you want to connect to in the Computer box.
Configure any other desired options, and then click Connect.

Solution from the page at this link