I logged back in just as your above note was coming in to say that I had been too hasty in saying that everything was OK.
I did see the "unread emails" count increase by one in the folder where the eCart messages usually go, and assumed that it was the eCart receipt, but it was not. (The Authorize.net receipts did arrive)
In fact ... I have received neither the eCart confirmation mailing nor the self-designed Thank You letter I created and want to send.
Sorry for my error of assumption. I should have physically checked first, and not assumed eCart had done it.