Without loading this into a Web page, there are a couple of things it could be,

If there is a 1px space between the submenus, the menu will close when you roll over it.

The other common problem is te css for hovering.

As for menu overflow...there is really no foolproof way to do this. I would suggest having the browser check the width of the window vs. the position and width of the menu and reposition the submenus on overflow.

Your best bet is to design your site in such a way that this situation does not happen or happens only under certain conditions that can be easily avoided.