Hi,
I've tried three orders on your website. For all three orders, the orders were created a the end of the checkout (I got the notification email). For one order I saw the thank you page. For the two others, I was logged out from the website after the order was created (and thus lost the cart and was redirected to the products listing page).
So the conclusion is that there is some kind of plugin which logs out the customer after the checkout.
I suppose that it is because the customer is being added to some user group, and that the plugin has to log out the customer so that he gets the new user group when he logs back in.
It could come from a mass action you created or the way the HikaShop user group after purchase plugin is configured.
Check all that and try to disable them if you have any enabled and try again.
It could also come from a third party plugin so if it doesn't come from mass actions or the user groups plugin, check the different plugins of the groups hikashop and system on your website via the Joomla plugins manager.