I've just tested mine, and it works good. No problem at all.
After I close an Open Ticket become Closed ticket, then at the bottom of the viewticket page, the checkbox become "Reopen on Reply" and the status become "Closed"
I also checked this Close Ticket from the "View Closed" list, it does exists there. Also when I search this closed ticket by using search feature, and after found, I click to show detail, the status is Closed. It means: no problem with mine.
Best regards,
Masino Sinaga