Hi Jolandi,
The not scrolling problem in the mobile menu is not related to HTTPS/SSL at all. Our theme default feature of the mobile menu does work and scrolls with no problem as you can see here:
http://demo.theme.co/integrity-1/
The problem with your installation is that you added a custom code to force the mobile menu to stick to the top of the screen and that is causing the problem and forcing the menu to NOT scroll.
Please bring back the original feature of the theme which is to have NONE sticky mobile menu and it will scroll as you expect.
Customizations such as making the header sticky in the mobile view is outside of our support scope and whatever side effect the custom code might cause will not be under our responsibility to fix.
Thank you for your understanding.