I've been using WP Super Cache and Ubermenu successfully together without any issues using this in my code:
<!-- mfunc wp_nav_menu(); --> <?php wp_nav_menu(); ?><!-- /mfunc -->
This is mentioned in an updated: http://wpmegamenu.com/help/#faqs
Potential Solution
One potential solution is to use the caching plugin mfunc functionality. For example, in WP-Super Cache this may help (different plugins may use different syntax, check your caching plugin's documentation for details on "dynamic caching")