Hi,
Well, the plugin cannot really control that, it just prints whatever the theme returns. I think the live loader jQuery selector might be too specific, the no-results template within the theme changes the whole main area. You might have to change it from
.place-listing-section
..to:
#main
..like so: https://i.imgur.com/oZ9WQLS.png
Using the other one would be better, if the theme printed that in the no-results template file (search.php template). Optimally, that item should be present there, and the plugin would copy it’s contents.