The 1- to 2-month-old calf was first sighted Sunday in waters off north Sydney, and on Monday tried to suckle from a yacht, which it would not leave. Rescuers towed the boat out to sea Monday and the calf finally detached from it - but the creature returned to an inlet near Sydney on Tuesday.
A second attempt to lure the whale out to sea Wednesday also failed, with the calf refusing to follow the wildlife officials' boat, a spokeswoman for the Department of Environment and Climate Change said.
Unless the whale finds a lactating female to accept it, it will die - probably within days, said the spokeswoman, who spoke on condition of anonymity, as is customary.
"We haven't given up on the whale, but he does appear to be weaker than he was yesterday," she said.
An expert from Sydney's Taronga Zoo was examining the whale to assess its health.
On Wednesday morning, another yachtsman reported seeing the calf attempt to suckle his boat and two others.
"It sounded like a bit of a vacuum cleaner on the bottom of the boat. I finally got up and here's this whale suckling the side of the boat," Peter Lewis told Fairfax Radio Network. "It was a very, very sad sight. It did it for about an hour, going from side to side on the boat and at times blowing air under the boat, and it just seemed to give a sigh out at one stage as if, you know, 'this isn't working."'
One Australian scientist suggested an artificial teat be constructed in order to feed formula to the whale, but environmental officials dismissed that as virtually impossible.
"They suckle for 11 or 12 months, so it's a long time - we'd just agree it'd be very difficult," the environmental spokeswoman said. "We think it really needs to find its mother or foster mother and those are really the only chances."