As far as I know, the timeout for authorization in OS X (if done properly) is set in the Policy Database located at
etc/authorization, usually programmatically. It looks like a plist file, and if an item has no 'timeout' key, then it has no timeout.
I do know that the preference is usually set in code using Apple's APIs (as shown in Apple's Authorization Services Programming Guide and the function reference).
This is a protected file. Use something like
sudo pico /private/etc/authorization to edit it.
The entry in this file will have a title using a kind of descriptor 'com.company.application.right' or something like that (e.g. com.apple.itunes.copy, com.stackexchange.superuser.deleteuser) - which is specific to each application, so look for that. (It's in alphabetical order to make things easier, I believe).
If there is no such entry, then the app probably grabs authorization in another way which I don't know about. I just tried adding a timeout to an app I wrote - it worked. I then deleted it again - and the timeout disappeared. It should work in your case, I'm guessing.
You do mention a settings panel - if that involves System Preferences then I don't know how it works either. There's no way to do it through applescript.
Edit: If there is no such entry
ANOTHER way an application may authorize is using the now deprecated and insecure method
AuthorizationExecuteWithPrivileges. I'm guessing that if an application doesn't have its own entry in the Policy Database, it uses
AuthorizationExecuteWithPrivileges. It may be that the application you're trying to work with uses this.
There is an entry in the Policy Database for this particular method called
system.privilege.admin, but note that modifying this and deleting the timeout will probably change the timeout for all applications using
AuthorizationExecuteWithPrivileges, not just the one you're trying to change. It may be worth a try.