Irene Nel, 73, came to visit family in Bristol on a tourist visa in 2012, but later became ill with kidney failure.
She has dialysis three times a week and her daughter, who moved to the UK in 1999, said she will die if sent back.
The Home Office said "all cases were carefully considered" but Mrs Nel cannot remain in the UK.
Initially Mrs Nel's medical insurance paid for her stay in hospital when she became ill. It has now said it will not pay for any further medical treatment but would pay for her to return to South Africa.
The case echoes that of 92-year-old South African, Myrtle Cothill, who had her threat of deportation lifted after more than 150,000 people signed a petition for her to stay in Dorset with her daughter.
Mrs Nel said she wants to remain in Bristol because she has no family in South Africa to look after her.
She is being cared for by her daughter Desree Taylor in Sea Mills and has two other sons who live in the UK, and have British passports.
Mrs Taylor, a British citizen, said they had done everything to help their mother stay in the UK legally, but their visa applications had been rejected.
Her mother said in her letter to Home Secretary Theresa May that if she is sent back she would like "six weeks notice so I can stop dialysis".
She said: "I'd rather die than go back there. I love my country but I cannot go back to nothing."
Mrs Taylor said: "I don't want to sit and watch my mum pass away but it's out of my control. I don't understand how someone could decide that on someone else's life.
"I don't know how I am going to deal with it that is why we're pleading for help."
A Home Office spokesman said: "All cases are carefully considered on their individual merits, in line with the UK immigration rules."
He added an independent immigration judge had "upheld this decision".
Desree Taylor said the family had spent more than Â£15,000 on legal costs and had now launched a petition with more than 1,000 signatures so far.
An elderly South African woman living illegally in Britain has written to the Home Secretary asking for clemency over her deportation.