The behavior I see may be related to the large number of posts (when a search is done, far fewer than the total number of posts are found). This sometimes causes problems on WP Engine hosted sites.
There is a setting to override a ‘feature’ of WP Engine hosting, that truncates long SQL queries (which ours are). Edit the site wp-config.php file and add this at the top, after line 1 (on a new line 2):
define('WPE_GOVERNOR', false);
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(also see here for another related support note about this – https://support.searchandfilter.com/forums/topic/killed-query-errors-in-log/#post-64826)
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