You have two choices, keep calling UA daily to see if award space opens up, or try using the ANA tool to identify when there is avaialbility. Remember to always be flexible with dates.

Specific to the DEN-NZ route:

1. Make sure to ask which filghts are the problem for the dates you are searching. That far out, it is common for agents to overlook Y for the domestic connections, or it may be that there are no award seats on the UA conneting flights.

2. If you are 1K, take any flights you can get (even in Y) and then call to improve those flights - no fees for changes as a 1K.

3. I have found that the ANA website is pretty accurate for NZ availability (at least for the SFO-AKL and LAX-AKL routes).

4. I think that NZ releases more seats 3-4 months out. I think that I read this on FT somewhere and it seems to be the case if you look on the ANA site (granted - 3-4 months from now isn't peak season).