Maddison Dawn Wilkins Jackson died in 2013 after staff at the Royal Shrewsbury Hospital could not find her mother a bed on the labour ward.
The health secretary ordered an investigation into maternity services at the Shrewsbury and Telford Hospital NHS Trust in April.
The trust says it has apologised to Maddison's family for her death.
A new report from the Royal College of Obstetricians and Gynaecologists says that poor care was responsible for hundreds of babies across the UK either dying in labour or suffering severe brain injuries.
The report's conclusions appear to chime with the experience of Maddison's parents.
There had been no hint of anything being wrong when Katie Wilkins went to hospital in February 2013. Her pregnancy had been smooth, and as she was 10 days overdue, she went to the Royal Shrewsbury expecting to be induced.
The labour ward was full, however, so Katie and her partner Dave Jackson were put into a side room.
Initial monitoring indicated their baby was healthy, but the induction didn't happen due to pressures on the ward. Staff kept telling the couple they would proceed when a bed became available.
"What stuck in my mind, was that plus term, the placenta doesn't work as well, so I knew time was ticking," says Dave.
Staff refused the family's request for Katie's waters to be broken in the side room, saying there was a risk of infection. After being awake for two days, Katie and Dave feel asleep.
Despite her medical records stating clearly, "Katie reports she is willing to be taken to ward 20 (labour ward) any time overnight", she remained in the side room for a further 15 hours.
No monitoring took place - either of her or her baby.
'We always wonder'
The following day, when staff tried to check on Maddison, they realised she had died.
"I can still hear him saying it now, we can't hear the heartbeat," says Dave. Immediately, Katie was found a bed and had to give birth to her daughter.
A letter from the trust in July 2013 said: "Sadly we have to conclude that had your induction occurred more timely, Maddison would likely have been born alive."
"We always wonder what colour eyes Maddie would have," wonders Dave, "because we never saw her with her eyes open."
"She was very tall," says Katie, "so we wonder how big she'd have become."
The family now want their case to be looked at by NHS Improvement, which is carrying out a review into how the trust investigated baby deaths and other maternity errors.
Maddison's death is at least the ninth avoidable death at the Shrewsbury and Telford Trust since 2013. Seven of the babies died in a 20-month period between September 2014 and May 2016.
A failure to properly monitor the babies' heart rates during labour contributed to several of the deaths, an error today's report from Royal College of Obstetricians and Gynaecologists has highlighted as being one of the main reasons for errors in labour wards.
In a statement to the Eyes On Events, Deidre Fowler, director of nursing at the Shrewsbury and Telford Trust said: "We met with Maddison's family following her tragic death in 2013 where we expressed how deeply sorry we were for the delay Maddison's mum experienced in her induction and to offer our sincere condolences.
"Following Maddison's death we made changes to our practices which have included improving advice for midwives around foetal movement and monitoring in line with national NICE guidelines and how we escalate concerns when women in our care experience delays because our maternity units are busy.
"We shared these improvements with Maddison's family at that time, but realise this will have offered little comfort to them."