Just a quick update, last night, I placed two separate orders and received none of the related e-mails (in my case with a Gift Card order, there should have been at least 3 e-mails total). I even checked my spam folder before posting about this problem and entering a support ticket.
This morning, I placed another order and immediately received the order confirmation in my inbox.
I updated the support ticket with these facts (and the fact that I had received my GC information from one of the customer liaisons that monitors the forums) and left it open.
I hope they will still investigate the issue to prevent it from happening again.