Kayak doesn't seem to have access to many of the lower fare buckets, particularly on Asian airlines. I seem to have this trouble on JL and CX too. I usually double check with those airline websites. Kayak is mainly useful for schedules across many airlines, and give an upper limit to lowest fare for an itinerary. But I don't rely on it for giving me the lowest fare.

Also, I think they cache airline fares periodically - it's common that Kayak or Orbitz it will quote one fare and it will either be higher lower, or unavailable when I try to book. Airfare algorithms are so hopelessly complicated that one search tool isn't going to do it. You probably need to get a few opinions.