Hi,
I'll suppose that you're using the Authorize.net payment plugin available by default in HikaShop (and not the Authorize JS plugin available on our marketplace), with the SIM mode activated (and not AIM). Can you confirm that this is the case ?
Supposing that my assumption is correct, you first need to check the status of these orders. Is the status changed to "confirmed" automatically or not ?
If no, then it's a payment notification issue. With the debug mode activated in the plugin, information about the payment notification issue should be logged in the "payment log file" available under the Files section of the HikaShop configuration. So checking there after a non confirmed order (with the payment appear on Authorize.net) should provide useful information about the problem.
If yes, then it would indicate that the payment notification is properly processed by the Authorize.net payment plugin but that the issue happens either in a plugin implementing the "onAfterOrderUpdate" trigger (I would suspect first a third party plugin or custom plugin, or a mass action not working / configured properly), or an issue with some email customization creating a problem. Either way, a fatal error message should be logged in the PHP error log of your server pointing at the file and line number where the problem is occuring.