Just some samples I tried:
Using Amadeus: Awards/Skyteam w/ POS: US-AF or FR-AF -
ICN-LAX 22 Mar 2012 (and v.v.) - No Award Availability/Route too complex/Date out of Range; KE should have some kind of flight listed

LAX-PVG 22 Mar 2012 (and v.v.) - Only CI or AF routing to PVG available. No mention of China Eastern (MU) for their routing.

LAX-CAN 22 Mar 2012 (and v.v.) - No Award Availability/Route too complex/Date out of Range; CZ should have some kind of flight listed. No mention of China Southern (CZ) for their routing.

These are hub flights, so there shouldn't be any reason nothing is available. Other dates also yielded same results.