If you are using the option to get a custom data form to launch automatically on login (option in agent configuration), then the form should appear for any user who logs into the device, however it will only do this up until a single user has filled it it. Once the form has been completed it won't show up again automatically for any users on the device unless the form is updated and rescheduled.
Other users can launch the same form manually from the start menu after it has been completed by the first user (if the option to see the menu is enabled) but they will see the answer that the first user had populated within it.
Custom data forms are really applicable on a per device, not per user type scenario.
Does that answer your query?
Maybe a permissions problem?
That's what I thought. But how to resolve it?
The custom form files reside in the directory: \\YOURSERVERNAME\LDlogon
Can the user that can't open the custom form navigate to this UNC path at all?
That's the first thing to be sure about before going down the line of thought of "permissions".
If the answer is no, then the next question is, can any user get to it?
If yes, then whats' the difference between the users that can and can not.
You'll need to dig into the permissions on your core and figure out what is going on there, or you may need to figure out what AD group membership that your user doesn't have in the event that it goes in that direction.
There should be some articles in the forum for more about permissions and what not.
Hope that helps!