Hi,
From what I understand, you have a problem with the loading of the products with the "infinite scroll" system which doesn't initialize the voting system for products loaded that way.
I check on our end and this is working fine.
So please check two things:
1. Edit your menu item via the Joomla menu manager, and under the "products options" tab, please make sure that the vote display option is activated.
2. Check if you have the file templates/YOUR_TEMPLATE/html/com_hikashop/product/listing_div.php via FTP. If you do, try renaming it in order to deactivate that view file override as it must be missing some bits of code to make that work properly.
If these don't help, I'm not sure what could be the problem. But you can edit the file "listing_div" for the view "product" via the menu Display>Views of HikaShop and change the line:
<?php if($this->params->get('show_vote')) { ?>
to:
<?php if(true) { ?>
and that should fix the problem.