This means that the Popup client was able to attach to the server, but the port was not available, or the Popup client couldn't resolve the server name.
Name resolution is a matter of ensuring that your DNS servers are all properly configured and that Forward and Reverse zones are working as expected. As a trial (not a permanent solution), you could add an entry to a problem computer's HOSTS file (use the name of the server as indicated in the Administrator) and see if the problem goes away.
Port access means that, potentially, you have a faulty component somewhere along the line; maybe even a proxy services issue (if proxy servers are in use on the network) or firewall problem. The best way to determine a problem is to install a packet capture tool (like Microsoft Network Monitor) and see if there is a server issue with that TCP port, or if it exists somewhere else on the wire. The workstation is your better install point, as you can more easily spot RST (reset) packets that appear to come from the server immediately upon communications start. If you do get RST packets without a FIN (end), then you're probably looking at a firewall or router issue. This can also be a timeout issue: does the client begin the session and it just stop there?
This should give you somewhere to start.