I have seen that with restricted users: at the end of the day, the license leased must be stored somewhere locally, so in very tightly secured environments, where the user is not able to write on the Windows Registry
or some folders like
keeps while the session is open, but after logging off, all information is removed from memory.
I'd suggest you to use both the Desktop and File / Open in Server and the Plugin in IE to log into the AccessPoint, be able to open a document, therefore borrowing a license that has been assigned correctly.
Check the History tab in the QMC, System, Licenses, QlikView Server, Client Access Licenses just to make sure that the Server is actually leasing and keeping track of the licenses assigned.
Hope that helps.