What parallax mapping plugin are you using? Which RM are you using, MV or MZ? Normally it should be compatible with item scene and parallax map (the default one).
Let's start from how do you reproduce this problem. I started the test using Galv's master demo and added UT_PreserveMapScene to the plugin list. When I started the game and went to the layered graphics map, opened and closed the menu, every thing seemed fine.
But it appears you are not using the standard UI? I see you have some Hendrix plugins which are related to the menu, maybe I should test with them with layered graphics. But if you have a valid demo it will make my life easier, considering you are using quite a lot of plugins, I need to find and set them up.