Our Development team noticed that the website’s Custom CSS files are not loading on the pages where Responsive Menu is not working. And the HTML is also not from Responsive Menu plugin.
The only real way to diagnose where the problem lies is to disable all plugins and see if that fixes it. If it does, then you need to enable the plugins again one by one until you find the offending plugin.
If that doesn’t fix it, then you need to try and switch themes, if that fixes it then we know the theme is the issue.