Hi,
First, please check the menu Customers>Emails history and check if you see the emails there.
If you see them there, then HikaShop sent the emails to the email server and the problem is not linked to HikaShop. You'll have to contact your hosting company to have them check the log of the email server for the email (you can give them a screenshot of the details of the email in the Customers>Emails history menu so that they know what to check).
If you don't see them there, then yes, we can have a look in your backend. We'll need that you also provider the order number so that we can check the situation. You can send the information via our contact form along with a link to this thread:
www.hikashop.com/support/contact-us.html