Hello Fred,
normally it requires that you assign the menu to a position of the mobile template of Responsivizer, such as 'responsivizer_mainmenu'
If you have already an instance of the module for the desktop template using the button 'make mobile' you can easily migrate it to the mobile layout.
The menu management for mobile is explained in great details in the pdf docs at the partagraph 'Mobile menu positions and management' and an example is visible in the video:
https://youtu.be/B1fqydcZYlI
Cheers,
John