I've only had a very quick look and here's what I noticed:
Everything is controlled by the SavExit Global variable if this var has a value of 1 then the menu will be destroyed.
Everything selectable on the menu sets this var to 1.
So from that point on the save/load menu is destroyed upon creation.
Try adding a System => set SavExit to 0 action right at the end of event 3 in "SaveLoadScreen"
It will work **.
This resets the var value to 0 upon completion of a valid destroy routine so because the var SavExit is 0 the event at 3 is not met (SavExit=1).
** There are better ways of achieving your aim see comment two...