An 80-year-old Taylors Lakes woman and her autistic daughter face the prospect of deportation next month, after their appeal to the Immigration Minister for compassionate intervention was rejected.

Florence Allen and her 50-year-old daughter, Sheryil, migrated from India in 2012 to be closer to family members, who act as the primary carers for the pair.

The Allens have about 80 family members in Australia, with all of them now Australian citizens or permanent residents. They have no family left in India, should Florence and Sheryil be forced to return.

It means Sheryil faces the prospect of spending the rest of her life in an Indian institution.

The pair have been on bridging visas for five years, but Florence’s application for permanent residency was rejected because she has a dependent child with a disability.

Florence’s son, Elroy, said the prospect of having the tight-knit family torn apart was heartbreaking.

“It’s quite a stressful situation at the moment,” he said. “We’re a very tight family, and Sheryil has been the glue that has kept our family together. She is well loved by all her nieces and nephews … she has never known a life without family.

“We were told we had a very strong case for ministerial intervention on compassionate grounds. We’ve provided documents from schools, churches, community groups, shown how we provide private health care as a family for my mother and sister. We don’t want any welfare money or government assistance – we just want to keep our family together.”

The family pays for private health insurance for both Florence and Sheryil, and also pay fees for Sheryil to attend a day care program in Sydenham.

Florence said she would be unable to care for her daughter if they were sent back to India.

An online petition calling on Immigration Minister Peter Dutton to intervene has collected nearly 30,000 signatures.

The family was last week informed that the Assistant Immigration Minister had rejected their appeal for intervention, saying it was “not in the public interest to intervene”. A spokesperson for the department of immigration and border protection said the case had been “comprehensively assessed”.

“The assistant minister cannot be compelled to exercise his powers and he is not required to explain his decisions,” the spokesperson said.

“The assistant minister only intervenes in a relatively small number of cases which present unique and exceptional circumstances.”

Florence and Sheryil have been given until October 3 to depart Australia.

Elroy said the family was despondent, but was still pleading with the minister to reconsider.

“If they go back to India it would cause irreversible psychological damage for my mother and sister, and the whole family,” he said.

“We’re running out of options – we really need the minister to reconsider for the sake of our family.”