Hi rjcowan. The mobile menu icons, along with the sidebar icons, are all driven by javascript. Might be a conflict with one of the active plugins. You could try deactivating all the plugins and see if that fixes it. If so, reactivate the plugins one at a time to determine which one causes the problem.
I am having the same problem on my iphone5, disabled all my plugins but mobile menu still doesn’t drop down on index (blog) page only. Single pages work fine. Using Hueman, latest version.
http://www.devault-design.com/marygrady/
Finally found the culprit – Gallery plugin. The only plugin i didnt install myself.
anyway thanks for the advice.
Found my problem! I had an extra front-page.php file in my child theme folder. The conflict thought put me on the right track though! Thanks!