Immigration Minister Peter Dutton has refused to intervene in the case of the Lees, despite thousands signing a petition to stop them being thrown out of the country.
The Department of Immigration and Border Protection advised the family in a letter that their final appeal for intervention by the Immigration Minister had failed.
"The department has assessed that this request does not meet the guidelines for referral to the minister," the letter said.
Byran Lee said he is devastated by the decision.
"Someone can just decide our whole future within two days...this one guy. It's shocking. I am just crushed," he told SBS World News.
The Lees had urged Immigration Minister Peter Dutton to intervene after a migration scam swallowed up more than hundred thousand dollars of the family's savings.
The migration agent hired by father David Lee to get him permanent residency instead fled the country with the money. Subsequent visa bid extensions, involving the Administrative Appeals Tribunal, failed due to what the family said was poor legal advice.
The plight of the Lees has led to more than 6,000 people signing an online petition started by their local Catholic Church, St. Christopher's Parish Syndal.
Patrick Jackson from the local church said it hard to see the family experience such hardship.
"They are very hardworking members of this parish and it's a real tragedy that they have been slapped down," he said.
A spokesman from the Department of Immigration and Border Protection said the Lee family's case has been carefully considered.
David Lee, an IT engineer, has run a series of businesses and was recently granted an innovation patent for a web-based device he invented that can control home appliances.
His wife Jessica works as a piano teacher.
