Just completed mine. Then started reading this thread and went back to check on it. My status said "open" and then when I came back to it again after hitting a few different pages on the site, there was no column in that spot any more.
I have not recieved a 3rd email either, but it's been maybe 30 minutes since I completed it. It is the middle of the night after all.
Also noticed there was no area where they asked if I had prevously interviewed with SWA. Does this mean I get a clean slate? Most likely it will ask in the more detailed application if I get the elusive "3rd email" tomorrow.