A five-year-old girl with a history of asthma was turned away from seeing her doctor because she was "late" - and died that night in hospital.
An inquest heard Ellie-May Clark was not seen by Grange Clinic in Newport despite having an emergency appointment because it operated a "10 minute rule".
A chance to "provide potentially life-saving treatment was missed" said the coroner, giving a narrative verdict.
After the hearing in Newport, Ellie-May's family said "she was let down".
Ellie-May's mother Shanice Clark told the inquest in Newport she requested a home visit when her daughter began wheezing and was unable to walk home from Malpas Court Primary School in January 2015.
Instead, she was offered an emergency slot for 25 minutes later. She said she told the receptionist she might be late as she had to arrange childcare and catch a bus.
Ms Clark said when she arrived at the surgery in the Malpas area of Newport she was five minutes late for her 17:00 appointment but had spoken to the receptionist by 17:10.
But this time was disputed by former receptionist Ann Jones who told the inquest she believed it was 18 minutes past five when the doctor was informed that Ellie-May had arrived.
The child's mother was then told by GP Dr Joanne Rowe, a partner in the surgery and its lead for child safeguarding, that she would have to return in the morning.
However, the coroner heard this was the first time the rule had been imposed on an emergency appointment.
Ms Clark said she was "angry" and "upset" when they were asked to come back. She said Ellie asked: "Why won't the doctor see me?"
Dr Rowe did not ask the reason behind Ellie-May's emergency appointment, or look into her medical notes before refusing to see her.
The hearing was told Ms Clark continued to check on her daughter at home every 10 to 15 minutes and at about 22:30 she was coughing.
Ms Clark said Ellie-May then fell off the bed and was turning blue. She was taken to the Royal Gwent Hospital in Newport by ambulance but died.
The inquest was told that the cause of death was bronchial asthma.
Wendy James, senior coroner for Gwent, recorded a narrative conclusion and said it was "not acceptable" for Ellie-May to have been turned away from her emergency appointment without any clinical assessment or advice for what to do if her condition worsened.
"From the evidence before me, it is not possible for me to determine with certainty whether an earlier intervention would have altered the outcome for Ellie but nonetheless Ellie should have been seen by a GP that day and she was let down by the failures in the system," she said.
"Ellie-May Clark died of natural causes where the opportunity to provide potentially life-saving treatment was missed."
The family released a statement and were "disappointed that a finding of neglect was not reached".
"The family acknowledge an apology from Dr Rowe, especially as they have been waiting in excess of three years for an outcome and to receive answers to their questions," said their lawyer Justin Chisnall.
The coroner will write a report to the clinic and the local health board to address the lack of an effective and robust care plan for Ellie-May.
A spokesman for Aneurin Bevan University Health Board said it would be "inappropriate to comment whilst we await the coroner's report".