I’m using the Multi-level Navigation Plugin in my site – http://www.comm-it.com.
I changed the CSS and add borders to the drop-down menus.
When the page is being loaded, it draws these borders for all the items, and I can see it if the connection is too slow – see the attached image.
I’m not sure what the solution to your problem is sorry. If you sign up for Premium Support I’d be happy to investigate further or even code a custom menu which loaded the various sections of CSS seamlessly for you, but bug fixing something that specific is too time consuming for me to do for free sorry.