Nowhere in the GSX code there's anything that stores the menu position, but it's surely saved by the simulator, since when you move it around in the normal screen, the last size and location used IS saved but again, it must be something done by the sim internally, we surely haven't coded any behavior to save or restore the window position and location.
Now, why its docked/undocked status and/or the location on the 2nd screen is not saved, and why you say it is saved with other toolbar windows, we cannot possibly know, because you must understand the whole HTML/JS menu system is completely undocumented and, before dwelling into trying to fix this, it might be best to wait for some documentation to appear. According to Asobo, the SU12 SDK should include a first draft of the HTML/JS documentation, so we'll surely have another look.
