Thank you RixStix for the clue I needed.
To anyone searching for a solution to this problem here is what I learned.
In spite of what it says in the zen-cart tutorials and forums, I needed to put in a URL into the Authorize.net response/receipt settings for Default Receipt URL. I used the value suggested in the zen-cart Authorize.net SIM module, it can also be found in your log files as the value for [x_receipt_link_url] =>
https://your_domain.com/foldername/i...eckout_payment
It is my understanding that the URL in the Authorize.net settings must match the URL that zen-cart sends as its [x_receipt_link_url].
I set the receipt method to POST.
Without this URL in the Authorize.net settings, I observed that transactions were going through, authorize.net receipts are issued and payments accepted, but the zen-cart was not recording the orders. When the URL's are set up correctly, the authorize.net receipt page shows a prominent button labeled: "Click here to complete this order." Only after this button is clicked will the order register with zen-cart, so it is possible for a user to create the missing order problem by simply not clicking the button.
Hat tip to RixStix for pointing out the other problem I have been facing. Authorize.net SIM cannot be tested when your store is in down for maintenance mode. Everything does test correctly and orders do appear when Authorize.net is placed into test mode.
Good luck out there
Kev