Originally Posted by ckpeter

Actually, I have experienced this a few times.

Never figured out what the problem was, but my suggestion is to call again (up to 3 or 4 more times), wait a day or two and try again, and to ask the agents to search segment-by-segment, but in sequence (so, ask for the international segment in the beginning, then if the agent found availability, ask for the connecting segment to be added).

Just be advised that the CX availability may well be phantom and non-existent, so don't get your hopes up too much.