"That's why I named her Eva. Because I thought it sounded like it was an angel's name.
"It wasn't until later the nurses told me it means 'the living one' - it means life."
Eva, now 4, has had several operations to repair her diaphragm. But each time the hole has reappeared.
She has complete gastrointestinal failure, meaning she has to be fed through a tube.
The last time she went home to Warkworth was in May 2009. The rest of her life has been spent in Auckland's Starship children's hospital, where doctors have to monitor her condition daily.
"It's been traumatic at times, of course," said Ms Mitchell. "It's not very often, but sometimes I'll have a cry and Eva will ask me, 'Mum, why are you crying?'
"I'll tell her that sometimes mummy doesn't want her to be sick any more. She'll look at me in shock and say, 'Am I gonna be sick?'
"For Eva, this is all normal. The hospital is her home. She doesn't know anything else."
The family, including dad Joel and older sister Mela, who is 6, have had a lot of support from children's charity Cure Kids, which funds research for children's life-threatening illnesses.
Ms Mitchell, who loves to paint, is auctioning about 30 original paintings done over the past five years - starting from when she was told her unborn baby was not expected to live.
The paintings are symbolic of the family's journey and particularly of Eva's life.
The auction will be at the Pullman Hotel in central Auckland on Saturday and money raised will go to Cure Kids.
Ms Mitchell said: "There probably is no cure for Eva, but there is hope for other children. I've had four years with my little girl. I never thought, and was told I would never have those years, and that is due to advances in medical care."
ON THE WEB
For ticket information or to donate visit curekids.org.nz.