Hi,
Thank you for the details, but we cannot replicate the issue on our end. I also tried the back-end demo, to see if there is any issue with a production: https://ajaxsearchpro.com/admin-demo/wp-admin/
It works there as well.
Does this appear on the back-end preview window as well as the front-end? If only the front-end, then clearing the browser/page and object cache may resolve the issue.