Yes, I have had this experience, but I was using gift cards. With certain* gift cards, you must book on the phone. I bought tickets for two people, but agent only booked one. It was a total clusterfuck. I had to call SWA's Customer Service line in Dallas. It was finally resolved, but not to my satisfaction. IIRC, we had to pay a higher fare for the second flight, even though it was their mistake and their unwritten (on the gift card) rules.
Call Corporate Customer Service and be persistent. For sure get a written confirmation of your flight and keep checking it. It's not really your problem that your card hasn't been charged, it's theirs to figure out. Not saying you should get free tickets, but let them worry about finding the money you obviously gave them.
*I get Coinstar gift cards on a regular basis. There is no fine print on them, but there should be. SWA says you can't use more than four in a single transaction, which sucks if they're small gift cards. There's some other unprinted gotchas, but off the top of my head, I can't recall. Obviously, I don't choose that option any more.