Thank you!
I can see the problem now. Something is altering the AJAX output of the search, it is adding extra HTML tags (paragraphs) to the output, see the output here for example: https://i.imgur.com/e11cgH6.png
I presume it is the translation plugin. While ajax search pro can deal with some level of error in the output, this completely alters the HTML, making it invalid, and can not be rendered properly.
Unfortunately this is not caused by the search, you may need to ask the translation plugin authors on how to exclude certain requests from the translator, as it does not handle it correctly in this case. If there is no option to do so, and there is any programmatical way they can suggest, let me know, and I might be able to help with that.