We had a similar issue with a custom theme. Sometimes the menu is not rendered completely. But after a refresh it works. So don't know what's happening with your theme.
Can you reproduce this on your development environment? If so, then try a default mendix theme. If not, it will be difficult for you to know what's going wrong.
I have the same issue when I'm NOT at office and when I'm connected with vpn to our office. Our mendix app is hosted in the same environment. When I visit the app in the browser (still connected with vpn) I only see the logo. When I disconnect vpn it works again. Don't know if this is related to your problem.