The top menu fixed and always visible on scrolling is also an option of the Responsivizer top menu settings.

You see both options in the screenshot attached. The position to use for the main menu is 'responsivizer_menu_top' as included in the second screenshot. Of course it must not be the same instance of the module used for desktop template. So just create a separate module instance for the main menu to use it only for Responsivizer template, so they are independent... that's obvious.

John