I had the same problem! It also appears on the Demo site of Quark.
Now I added this plugin which perfectly does the trick: https://www.ads-software.com/plugins/black-studio-touch-dropdown-menu/
It adds a javascript behavior on menus for touch devices so that they behave the way natively adopted by iPad / iPhone starting from iOS version 5.
@ahortin, just one more thing regarding Quark. On the demo where there is a drop-down menu it shows the icon “fa-angle-down” at end of the parent’s name so that it’s visible that there is a drop-down. On my site this icon doesn’t appear. Do you have an idea why?