I have had a look in the admin and I cannot see open the theme files (search.php in this case) to see what it is doing. However, I may have a better idea anyway; using Visual Composer (your version is old and should be updated, although I think they are about to release a new version for compatibility with WP4.9, and the plugin has been re-named to Page Builder).

The reason for my suggestion is that we have an addon plugin for Visual Composer. You can read about (and use the download link for) here in this post:

https://support.searchandfilter.com/forums/topic/can-we-change-template-desing/#post-136727

Hi

I see that your site has over 10k posts, and many custom fields on these posts.

I have made some setting changes so I can see the count of each category term in the select box and to hide those that are empty. You can see no terms are listed. This means that none are in the cache.

Can you try building the cache and see how long that takes, and if that makes any difference?