This is not an issue that we have been able to reproduce.
is not in any way related to closing tickets, I would only expect to see this operation called in the Admin view, and if it was the cause of the User not closing the Request it would have appeared as a popup at the time.
Some information on how the Users are trying to close tickets, what happens when they do, any errors or other messages etc. would be useful here.
As a final note, the Super User role should not be applied to any User who uses the system on a day-to-day basis, this should be reserved for the System Administrator account (or a similar User) where it would only be required to access the system and reset settings if something catastrophic happens.