When you've reached maximum number of connections using your remote desktop connection, for whatever reason, there is a simple solution to take care of this error. All you have to do is log in using a console command [to follow] and then open that computer's task manager, go to users, and then log off enough users that the remote desktop connection lets you log back on.
Here's the command:
mstsc -v:0.0.0.0 /f -console
[of course you'll replace the 0.0.0.0 with the ip address of your remote server]