The CEO of Bristol's NHS Trust has written to the parents of Ben Condon to accept failure to give timely antibiotics contributed to his death.
Ben Condon from Weston-super-Mare died at Bristol Children's Hospital in 2015.
Robert Woolley, Chief Executive of University Hospitals Bristol NHS Foundation Trust has apologised.
"I would like to publicly apologise to Mr and Mrs Condon. We failed to take the opportunity to give Ben timely antibiotics and this contributed to his death.
"I am also deeply sorry for the additional distress and hurt caused by the wait Mr and Mrs Condon have endured before receiving this explanation.”
17 February 2015 Ben Condon was born at 29 weeks at Southmead Hospital in Bristol
He spent seven weeks in the paediatric intensive care unit
7 April 2015 Ben came home with his parents - Olympic sprinter Allyn Condon and his wife Jenny
Two days later Ben started coughing and sneezing and was taken to Weston General Hospital
10 April 2015 Ben was transferred to Bristol Royal Hospital for Children after becoming lifeless and struggling to breathe
3pm 17 April 2015 Ben was prescribed antibiotics
8pm 17 April 2015 Antibiotics were administered - by then Ben had suffered a cardiac arrest
9.07pm 17 April 2015 Ben died having suffered a second cardiac arrest after developing acute respiratory distress syndrome
Earlier this year, Mr Condon brought a claim for clinical negligence against the Trust on his son’s behalf, based on the failure to give Ben antibiotics on 16 April 2015.
The Trust says it "has extensively reviewed again the circumstances of Ben’s death" and has obtained additional expert evidence and advice.
"Following this thorough reappraisal of the circumstances of Ben’s death, the Trust believes that it missed an opportunity to provide Ben with timely antibiotics and that this failure contributed to his death."
The Trust says the delay in clarifying its position is because medical experts "have a range of different views on whether and when antibiotics should have been given to Ben".
The Trust says it has made changes to the way it operates but recognises mistakes have been made.