I like using twentytwelve for some projects as it’s clean, and I know the CSS really well. In early September 2014 an update for twentytwelve was released. After updating the theme, the mobile menu stopped repsonding to clicks. Seems that a slight change in the coding for twentytwelve theme rendered it none-operational. This is for child themes with a custom header.php of course.
Go to line 47 or there abouts and find the line
<h3 class="menu-toggle"><?php _e( 'Menu', 'twentytwelve' ); ?></h3>
Replace it with the new line from updated twentytwelve header.php file
<button class="menu-toggle"><?php _e( 'Menu', 'twentytwelve' ); ?></button>
Hope my “hours” of troubleshooting helps someone.