There is no system variable that I know of that would control the visibility of that dialog window. You probably moved it off screen and it is sitting, unknowingly, behind your AutoCAD screen.
But just to be sure we're talking about the same thing, if you right-click on a Layout tab the fly-out menu appears with the words New Layout at the very top and four lines below that is the Move/Copy option. The fly-out menu appears but when you select Move/Copy you do not see a much smaller rectangular dialog box. Is that correct?
If you can't find the dialog box and don't want to do a REPAIR of the installation (the least invasive option) then the only other remedy I can think of is a custom lisp program called TabSort by lisp guru Lee Mac. It is described thusly....
A program designed with the intention to aid in the organisation of
layout tabs in a drawing, the program enables the user to
organise each layout tab using intuitively engineered buttons to move
selected tabs up/down or to the top/bottom of the tab order.
The program also offers the ability to rename a layout tab by
double-clicking on its entry in the list displayed, and furthermore
add a prefix and/or suffix to selected/every layout tab.
A facility is also provided to add & delete layout tabs, and also sort the tabs into alphabetical, numerical, or
architectural order; or reverse the order currently displayed.
A Find & Replace functionality is also offered to allow the user to quickly replace a text string in multiple layout tabs.
The user may also copy selected layout tabs, or set the selected entry as the current drawing layout.
A Help Dialog may be shown upon pressing H at the Main Dialog interface.
The program can be downloaded from here...
http://lee-mac.com/tabsort.html
Edited by John Connor - 01.Dec.2016 at 14:43