First off let me say, I think your theme is great! I have worked with several themes & this is one of my favorites.
My issue is that some of the icons I have set in my mobile menu are not appearing. I have several categories and the icons are set for all of them. Certain top level categories are not showing the icons as well as some of the sub menu categories.
Not sure what the issue is. Seems like something is wrong.
Please deactivate all the 3rd party plugins and activate only theme-required plugins on the site and then check the issue. I am sure your issue will be solved. Then Activate the 3rd party plugins one by one and check which plugin is creating the issue for you.
Otherwise, if the issue still exists then keep the 3rd party plugins deactivated and let me know I will further check on your site and give you a possible solution.