Hm. JFK-FRA works, JFK-SIN doesn't. SFO-(AKL|SIN|BKK|BJS) don't, JFK-WAW doesn't, DEN-MEX doesn't, JFK-YYZ doesn't. So, US-US, US-Western Europe, US-Australia. Strange dataset.
SFO-AKL has direct flights though. I know, I've done it. NZ8. Nice plane.
edit: Actually I checked and "sfo to akl" does in fact give me results.
Oh, and it's in a 100-seat all-business-class A340-500. I'm guessing they couldn't do it with a fully-laden economy section. Then again I'd hate to fly 19 hours nonstop in economy.