Have the On-demand extension objects been installed on that user's machine?
If so, can you try this:
* Open the On-demand extension object properties and note the details
* on the machine where it is not working, enter in a web-browser address bar http://<Hostname>:9001/help (replace Hostname with the contents of the Hostname field noted in the previous point. Also change to https if SSL is used).
* You should get something like the below
If not, you will need to investigate why. Probably a firewall (port needs to be opened) or DNS issue (try Telnet and/or nslookup) etc.
HTH - Daniel.