Please can you show us your site credentials so I can give it a closer look?
You are right it doesn’t work on responsive, there is a javascript error, but it seems to be caused by a third party plugin. Please disable any plugin added to check it they conflict.
The caching plugins are the culprit. I deactivated them and now the mobile menu shows up perfectly in mobile (tested in samsung s6 device and iphone 6+).
