Hello
I have observed that the placement of the Session.Input box isn't that random (but that doesn't mean it's logic, indeed): unlike the Session.Prompt that places at the center of EA's main area, the Session.Input box actually "tries" to place at the center of the "Scripting" window... or at the place where the Scripting window last was before it was closed.
If the Scripting window is at the center of the screen, you'll see the Session.Input box appear over it (I have tried doing several tests while moving the Scripting window from place to place on my screens : the Session.Input box follows the Scripting Window).
And it still works if you close the scripting window (the last position is remembered) !
If the scripting window is docked on the side of the screen, chances are the Session.Input box will only be partially visible and partially off screen.
Worse : if the Scripting window is docked on a screen side with auto-hide activated, the Session.Input box appears totally off screen.
An emergency solution to get it back is placing the mouse cursor over the corresponding input window icon you'll notice in the MS-Windows taskbar, wait for the window preview to appear then right click on it, choose "move", hit an arrow key on keyboard, move the mouse cursor to bring the invisible window back into visible screen area.

A better and long term solution is... not using the Session.Input method anymore and switch to Geert's VBScript InputBox suggestion.
Hope this may help.
Regards
Update : I have submitted it as a bug to Sparx through registered user bug report.