By design when items are dragged and dropped from the control they are removed from the source control. In order to customize that logic you will need to create a custom ListBoxDragDropBehavior
and override its DragDropCompleted
All you need to do is create a class that inherits the ListBoxDragDropBehavior class, override its DragDropCompleted and remove the call to the base method (leave the DragDropCompleted blank). The next code snippet shows how such DragDropBehavior should look like:
CustomListBoxDragDropBehavior : ListBoxDragDropBehavior
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