I think I see why its having trouble pulling it up.

On 4th July NZ64 departs 10:15pm, many hours after the latest arrival from Singapore. There is discounted economy available on this sector.
On 5th July NZ26 departs 4:30pm, but no discounted economy available.

Are you wanting stopover in Auckland or is it same day arrive in AKL head out to Tonga?

You can select SIN to TBU on the main page (without entering legs separately) if not stopping over in AKL.

Have you tried as separate tickets? One SIN-AKL return (this could be NZ once daily or SQ 1/2 daily) and the other AKL-TBU return. That prices out much lower (around NZ$3000 all up for a return date I picked at random) although higher than I'd expect.