The sailing yacht is well-equipped, with a tracking device, a satellite phone and an emergency buoy, which is meant to deploy automatically when a ship takes on water.
But not a single signal has come from the boat for more than three weeks.
Family members alerted maritime authorities in New Zealand in mid-June that the Nina was missing after wondering for days why they had not heard anything from Dyche.
Rescuers put out a notice to all ships in the Tasman Sea, requesting reports on any sightings of the ship. None came in.
The search from the air began, and it continues.
"While we have grave concerns for the crew on board Nina, we have not given up hope of finding survivors," mission controller Neville Blakemore said.