Toa, believed to be between 4 and 6 months old, was found stranded at Plimmerton on Sunday afternoon.
The Department of Conservation (DoC), Whale Rescue and Project Jonah - along with members of the public, boats and a plane from the Kāpiti Aero Club - have been out searching for his pod.
The searches have so far been unsuccessful, leaving the calf in the hands of Department of Conservation and Orca Research Trust staff for the past three days.
DoC marine manager Ian Angus said they plan to try to feed the orca a milk-replacement formula today to give it some nutrition.
"We've been taking a lot of advice from experts overseas who have got experience in this and we are just trying to work out what we think is a safe level of dosage."
Besides a slight lack of iron, veterinary reports show the animal is in good physical health, Angus said.
He said they remain optimistic after the reported sighting yesterday of a pod of orca near Raumati that looked similar to Toa's.
"We tried to go and see if we could locate it [yesterday] but unfortunately night came in and we couldn't, so we'll be aiming to go out on the water again later on today by boat and likely by air [then] we can follow up on that reporting."
DoC staff are focusing on sightings of orca between the Marlborough Sounds and the Taranaki coastline.
"[If you see orca] Please get in contact with us as quickly as possible, take some imagery even if we only get to it later and give us some sense of direction [they are travelling] because then we can follow up on that."
Angus said they are hoping the maternal bond between the calf and the pod keep them close by, but they're also considering expanding the search area.
He said members of Toa's pod have been studied for the last 20–30 years so DoC and rescue groups have an idea about how they behave.
"This pod is known to travel quite a bit so we are hoping as part of that normal behaviour they may start travelling back here."