The "survivor" might have been spared her ordeal if doctors picked up the disease, biliary atresia, earlier.
Miss Thornton took her 13-week-old daughter to the doctor three times before tests finally showed a dangerously high bilirubin count of 147 - a normal count in babies is 20.
Bilirubin is a body waste product processed by the liver which drains through bile ducts to the gut where it is ingested.
But as Miss Thornton and Mere's father, John Pomana, would find out, Mere's bile ducts were damaged because of the liver disease. It takes a special blood test of liver enzymes to detect the disorder and if caught early surgery is highly successful.
Mere was admitted to the Starship children's hospital in Auckland last June to undergo the Kasai surgery where part of the intestine is connected directly to the liver to drain the bile. By then she was 4 months old and the operation - which works best on babies under 2 months - was unsuccessful. Her liver began to fail and in July the family were told Mere would need a liver transplant, which she underwent last month.
Two days later, on January 17, the donated liver began failing.
Mere underwent a second transplant the next day but a week later she suffered an aortic rupture and her heart stopped for 30 minutes. Doctors warned she could die, be brain damaged or face dialysis but she has since recovered enough to move to a ward and eat her first solids.
Miss Thornton said the family were speaking out to warn other parents that liver disease could be mistaken for normal jaundice.
"You have to be careful because not all doctors or Plunket nurses know exactly what [biliary atresia] is. Fight for blood tests and do something about it as soon as possible."
Starship hospital head of paediatric gastroenterology Dr Helen Evans said the difficulty in raising awareness was that normal jaundice was common in newborns who did not have liver problems. "So the question is how do you identify the ones that have liver disease?"
Symptoms include if the baby is still jaundiced after two weeks, if their poo is pale in colour and their urine is dark, or if the jaundice appeared in the first 24 hours of life.
Dr Evans is researching with Otago University why New Zealand has double Europe's rate of biliary atresia and why the sick babies are not getting to hospital as soon as in other countries.