Once the clients browsers cache is cleared you should be able to see the updated application.
I have heard that some IT departments will cache files on a server to save bandwidth so that could be the problem, but it all depends on your network i guess.
One easy way to solve the issue is to change the URL of the application and have the old URL forward to the new URL. This probably not the ideal solution, but it might be worth a test to see if the client can see the new app.
Another test would be to have the user load the new app in a different browser such as FireFox or Google Chrome.
Finally, if nothing works you can add a query string onto the .swf URL defined in your .html page. You would open the index.html file on the server and where ever you see the file "index.swf" referenced you can change it to "index.swf?123456789"
The ?123456789 SHOULD cause the browser to think its a new file that has never been downloaded before and pull it down from the server. (Don't forget to backup up your index.html file first 🙂 )
Hope this helps,
Drew