I have compared the default WooCommerce archive-product.php file with the one from your theme, and there are many differences. But, what I can see, is that the theme one adds a sidebar in, but does this only if there are posts. Also, your theme template does not output the standard results list block if it thinks there are no results, or, at least, it omits the <ul class="products"> container.
Unless you can get someone to re-code that theme file, it means Ajax will not work.
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