I checked for availabilty using Continental/United miles for the route and dates you indicated. Business award seats at saver rate are available on July 27, flying on Austrian Airlines and changing in Vienna. Nothing is available on your preferred return date, but a saver award in Y is available the following day (August 5), taking a LH flight to Frankfurt and a Singapore flight from FRA to JFK. The first business saver award available is on August 7. There is a one-change flight via FRA on LH, and there are numerous available flights through various cities with two changes.

Hope this info helps.