Hi,
If you take a look at your browser console, you can see the result of the ajax calls.
I don't know why your server display warning messages, but that warning is displayed at the beginning of the JSON :
Notice: ob_end_clean(): failed to delete buffer. No buffer to delete in ****/administrator/components/com_hikashop/helpers/helper.php on line 1315
That's why the javascript cannot decode the json and do not display the sub categories.
To fix the warning (patch already ready in HikaShop), you can replace in the line 1315 of your HikaShop helper
By
But I will also recommend you to not display PHP warning in your webpages.
The display of such information should be done only under development context. It is more than recommend to turn it off for production websites.
Regards,