I haven't had this happen on DL but it did happen to me on TAP Portugal. I booked a flight and got a confirmation e-mail. So far so good.

When I showed up to check in, however, TAP did not have my reservation and made me buy full fare Y to fly. When I talked to customer service, they claimed they had sent an e-mail saying that my credit card never processed and that they cancelled the reservation. I never got this e-mail or I would have taken care of it. I asked them to refund the extra money I had to spend, but they refused. I talked to several reps, wrote letters, the whole nine yards. Nothing.

I no longer fly TAP, nor do I advise anyone else to (worst customer service I have EVER encountered). I now religiously check my statements to make sure the debit posts.