A family is fighting a decision that could see them forced to leave the country because their six-year-old child has a mystery illness.

Kai Tippett, from Lennox Head on the New South Wales far north coast, said his daughter Sienna had lived in Australia since the family moved from England when she was 10 months old.

He said the mystery ailment first became apparent several months later, and had affected her balance and speech.

"We started noticing when she was about 16 to 17 months old, she started having a little bit of a wobbly walk," Mr Tippett said.

"So from then we took her to the paediatrician, who then referred her to get more tests done.

"Basically she's got an undiagnosed condition, there is no label to it."

Mr Tippett said his daughter had had numerous tests and they all came back clear.

"She's quite headstrong, so she participates in everything an able-bodied child would, [but] she has slight balance issues and she doesn't talk," he said.

Mr Tippett said while he and his wife had had their applications for permanent residency approved, his daughter's had been refused.

"From the medical [tests], she got deferred on medical grounds, saying that she doesn't meet the criteria," he said.

"We were just devastated. It's one thing [having] to learn to come to terms with when you find out your daughter has got a disability, I mean it's a gut-wrenching feeling.

"But then you find out she's not welcome in the country she calls home, because of her disability.

"Sienna is learning Auslan sign language. That is only a sign language for Australia.

"So if she went back to England she would have to learn a complete new language to even be able to communicate with people."

Mr Tippett said the family had 23 days left to ask [Immigration Minister] Peter Dutton to overturn the decision.

Family 'appears to have good case', lawyer says

A spokeswoman for Immigration Minister Peter Dutton said he was yet to be given the details of the case.

The Department of Immigration and Border Protection said the family's ongoing request for ministerial intervention was currently being assessed by departmental staff.

Migration lawyer Nathan Willis said the family appeared to have a good case.

"This would seem to be one of those sorts of situations where the Minister should intervene for the sake of ensuring a just outcome for some people who have already got a pretty difficult situation," he said.

"They don't need it to be made more difficult by an arbitrary application of immigration law, which doesn't take into account that life is not always black and white."