The error is being caused by the theme. My guess is it stopped working when the site was upgraded to 3.6. Why? WP 3.6 registers its own
jquery-ui-accordion script and I'm certain the theme is registering its own using the same exact handle. Since WP loads first its script is registered first and prevents the theme's from registering therefor WP will load the script that is bundled with WP instead of the script theme expects which in turn is causing the script fatal error.
The solution is likely to search the theme files for a line of code that starts with either
wp_register_script( 'jquery-ui-accordion' or
wp_enqueue_script( 'jquery-ui-accordion' and change
jquery-ui-accordion to something that is more unique to the theme.
I hope that helps!