My team has access to a Windows Server 2003 server in the test organization that is built daily/weekly by script with the new product bits.  In order to meet our content deadlines, we need to run the GUI as it changes during product development and try to stay current. Well, as deadlines get closer, more writers try to remote into the server to do stuff. Often they are getting the error: "The terminal server has exceeded the maximum number of allowed connections". Typing this phrase into live search gives you this. Too-typical technical content- accurate, yet at the same time not remotely useful.

When you get this message while logging on remotely to a Windows Server 2003 server, it means that two RDP sessions are running on the server. This means that either two people are logged in and doing work, or one or more are not doing work, but still logged in. By default, you can have only two remote sessions and one console session.
To solve this:
Preventive: Get everyone in the habit of "log off" (not just close the remote window) when done working on the server. Play nice.
Reactive: If you need to get on right now you can force a logoff of the current user using the following command:

mstsc /v: yourservername /console

using credentials for a member of the local Administrators group or the Domain Admins Group
To delete existing connections:
Start > Administrative Tools > Terminal Services Manager.
Expand the This Computer node.
Click on your server name. 
Click on the Users tab and you should see all existing connections.
Right- Click on any session with a greyed-out icon (indicates that the session has expired) and select "Log Off" to kill that user/session and free up the connection.
To change the default behavior (limit of 2 sessions, no time out):
Start > Administrative Tools > Terminal Services Configuration
Select the Connections folder.
Right-Click RDP-Tcp (Microsoft RDP 5.2) and select Properties.
Select the Sessions tab and check the ‘Override user settings‘ option and set ‘End a disconnected session’ and ‘Idle session limit’ to 15 minutes. Set the ‘Active session limit’ to Never.

To avoid this problem in the first place and limit to one user at a time connecting to a Microsoft Windows Server 2003 terminal server in Remote Administration Mode remotely or at the console:-)

1. Click Start > Administrative Tools > Terminal Services Configuration.
2. In the console tree, click Connections.
3. In the right pane, right-click RDP-Tcp, and then click Properties.
4. On the Network Adapter tab, click to select 1 from the Maximum connections drop-down list.
5. On the Permissions tab, click Add, type Everyone in the Enter the object names to select (examples) box, click Check Names, and then click OK.
6. In the Group or user names area, click to select the Everyone group.

In the Permissions for Everyone area, click to select the Deny check box to deny permission for Guest Access, and then click OK.

Note This setting permits only one remote connection and only through the console, also known as session 0. To make a Remote Desktop connection to the server, use the mstsc.exe /console command to connect to the console session of a terminal server on a Windows XP-based computer or on a Windows Server 2003-based computer.