Yes, it does look like it's the sublevels. I've tested menu with up to 3 sublevels in my test site and the Navigation Collapsed works fine though. I've also added menu items and tested sub-leveling the SIMPLE X MENU TEST menu and it still works so I'll investigate deeper if this is a bug or not.
For now, as a specific solution for your site, you can choose 1 of these options:
- use the Navigation Layered (see secure note)
- if reducing menu items works for you, that would be another way
- rebuild your menu
If you didn't see the menu icon fields in Appearance > Menus, I'm sorry I temporarily added the script in this thread which disables the said menu icon options. I did that because the menu page is slow to load and removing the custom fields temporarily allowed for faster load time in the backend.
I removed the code after.