The Thai surrogate mother of the twins, Pattaramon Chanbua, says the couple abandoned Gammy, who has Down syndrome, and returned to South Bunbury with his healthy sister.
It has since emerged that the biological father of the babies is a convicted child sex offender.
The scandal prompted the WA Department for Child Protection and Family Support to launch an investigation into the safety and wellbeing of the sister after court documents showed the father had been jailed for abusing three girls in the late 1990s.
A department spokesman said on Wednesday that officers visited the house on Tuesday night but no one came to the door.
Officers reportedly visited the house again on Wednesday morning, and again failed to make contact with the parents.
In the latest twist to the story, a hospital spokesman in Thailand said that seven-month-old Gammy didn't have a life-threatening congenital heart condition as earlier reported, and his pneumonia was almost completely cured.
"We had a cardiology expert run a check on his heart and we are happy to say he has no heart disease to worry about," the spokesman from Samitivej Sriracha Hospital, where Gammy is being treated, told the Bangkok Post.
Prime Minister Tony Abbott distanced the federal government from any move to allow commercial surrogacy in Australia.
"I'm not one who generally thinks that the law should intrude into the bedroom," he told the Nine Network on Wednesday.
"This is a matter that is governed by the states. I don't want to make it even more complicated than it already is."
He said ensuring Gammy's sister was safe is also a matter for state authorities.
Thai medical authorities are threatening to take legal action against 21-year-old Ms Pattaramon because she accepted a $15,000 payment from the biological parents.
Thai health authorities say it is illegal to pay for surrogacy in the kingdom and anyone who agrees to carry a baby must be related to the intended parents.
The Thai medical council says it is investigating who delivered the treatment.
A family friend claims the parents were "heartbroken" to leave Gammy behind, believing he would not live more than a couple of days because of a congenital heart condition, and the mother of the twins has defended her husband as a good man.
Ms Pattaramon has said she wants the boy's healthy twin sister to return to her in Thailand, after learning about the father's previous convictions.
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