They did, as it turns out, ship us a replacement order when they never got any record of delivery on the original order. They shipped the re-order USPS Priority Mail on July 20, with a tracking number.
However, I didn't know that, because they STILL didn't notify me that the order had shipped, or send me the tracking number. I never heard a word out of them until I filed the PayPal complaint. I got email from them today with the tracking number; plugging that into the confirmation site showed a record that it was delivered Monday. It might have been sent out for delivery Monday; it didn't show up in our mailbox until today.
So, end of story: We did, in the end, get the pet tags we ordered for Shadow and Houdini. I doubt I'll ever do business with them again, because even though they did make good on the order after the first order disappeared, I hate dealing with a vendor who won't communicate, and trying to get communication out of this outfit -- even in response to a missing order -- is like trying to squeeze blood out of a stone. Communication is important, and these people aren't good at it.