Your configuration was correct, I have possibly found the problem. I've logged in via FTP and did a debugging on the search query code, and there some categories were incorrectly excluded.
I have fixed the corresponding code part, it should return results now as expected. Thank you for the correct log in and FTP details.
Also, I have noticed that you have lots of records. If I may suggest, you can try a different search logic (AND logic) to get better related results. The default (OR) logic setting is to maximalize the results count, but in your case I guess you would like better related results instead of lots of matches.
For more information, you can check this part of the documentation if you want: https://wpdreams.gitbooks.io/ajax-search-pro-documentation/content/search_logic.html
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