Thank you, but that did not work correctly. When I add this code, the header becomes sticky. . .but, when I scroll the page (which invokes the sticky behavior), the header does stick. .. but, then the menu does not function correctly.
Here is a quick screencast to show how the menu behavior changes when the "sticky" header is invoked - http://screencast-o-matic.com/watch/cDev2C1Uy4
We have tried to realize it with custom CSS, but it didn't help. It seems you need to change whole mobile menu structure via customizing the theme. We will try also improve this feature in the next updates.