In case anybody facing the same problem:
I found a solution for me. Add
.topmenu { display: block}
to Costumizer –> Additional CSS. Header/top-menu will be shown always; even on small screen sizes.
Note: Of course it just makes sense if your menu is quiet small. In my case i just have two items in the header menu (log in and registration). If the menu has more items it makes perfectly sense to hide it on small screens.
