I was just testing the plugin, and I got results around 0,2 seconds on average: https://i.imgur.com/PPtJVGj.png
Yet the response time was over 5 seconds still, which indicates an overloaded server. There are also 38 (!) plugins installed, including VC, WooCommerce, WordFence, ACF and other bigger plugins and a theme with a fully loaded editor – which in combination together require a pretty decent server to run smoothly.
I too am running some of these plugins on my demo environment (woocommerce, bbpress, acf, VC etc..), and a dedicated VPS is needed to maintain good speed.
I have also monitored other ajax requests to make sure that it’s not only Ajax Search Pro getting slow responses, and I have found that even the internal ajax requests are fluctuating up to 5-6 seconds or more: https://i.imgur.com/J8QBado.png
It strongly indicates that the server might be a bit too busy to handle all of the load at once.Best,
If you like my products, don't forget to rate them on codecanyon :)