The Problem

Can't remote desktop into Windows 2003 Server because connection was lost or didn't log out properly. Getting Max Connections error.

The Solution

In Windows XP / 7

START > RUN > (type) cmd ( hit Enter) > (then type) mstsc /v:255.255.255.255 /admin (hit Enter)

Obviously you'll need to replace 255.255.255.255 with the correct IP address of your server.