Bizarrely, the flight that I was asking for was the one that we ended up on anyway. As soon as she said it was waitlisted, I started asking whether the problem was due to married segments and that's when the penny dropped and she went off to do some digging.

Whether it was actually married segments or not I have no idea but they managed to do it in the end. It sounds like andypart got some duff agents who weren't prepared to go the extra mile.