Indeed, some requests were slower than expected.
I have modified the search algorithm file to a current test version, which should be faster. Currently I'm testing on the test page you provided, so far the results appear much fastear (in ~2 seconds)
However I can still see longer requests from time to time, which might indicate that your server needs more resources. I've tried for example the same search term several times, but the response times varied from 1 to 10 seconds. The request times went up drastically when I opened the back end of the site. If your traffic went up, you should definitely consider using a faster hosting plan. The search performance tracker also showed interesting values – the same requests took 0.09 seconds, then 5.3 seconds, then 2 seconds, then 0.09 seconds again.
This was also visible when refreshing some of the pages – sometimes it was quick, sometimes it took 10 or more seconds.
Anyways, the update I provided should make the responses faster, but I recommend checking if the hosting plan limits are enough.
Also, there are a few tips you can find in the documentation, which might be useful for performance tuning: http://wpdreams.gitbooks.io/ajax-search-pro-documentation/content/performance_tuning.html
Let me know if you have any questions.Best,
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