OK, after considerable mucking around on my test site, disabling or uninstalling every little thing I still had the problem. Turning cache off on my system and the problem goes away.
So, I went back to the Eximium demo install and turned cache on, voila! The problem manifests itself on the demo.
Can you please try on your system as you did above but turn caching on. Once you reduce the screen size to the point the Feature menu goes away do a browser refresh, I believe you will find the Feature menu re-appears.