After a bit more experimenting it seems to be something to do with the “ACF Content Analysis for Yoast SEO” plugin. It seems to load the admin-ajax.php on every keystroke. After upgrading to the latest WordPress the console errors went away on our site but the admin-ajax file was still being continually polled. There is now an issue about it on the plugin forum: https://wordpress.org/support/topic/admin-ajax-php-loaded-on-every-keystroke/
