When you close the dual-display the folder it was showing is forgotten. When/if you open the dual-display again it will choose a folder based on your preferences, which -- depending on configuration -- could mean it picks the same folder as the first display, uses a fixed folder, or chooses a folder from Smart Favorites.
You could ask GPSoft to add a feature which remembers the dual-display's folder whenever it is closed (either by closing the whole lister or just the display). This would be similar to the feature which remembers folders, window positions, and so on when a lister is closed.
I suspect you'd want such a feature to remember the directory individually for every lister, though, right?