Both families believe mistakes were made at Crosshouse Hospital in Kilmarnock, East Ayrshire, and they are calling for answers about the treatment received, the BBC reported.
NHS Ayrshire and Arran has apologised for any “failings they experienced during their time with us”.
Between 2008 and March 31 this year, there were four Significant Adverse Event Reviews concerning stillbirth deaths at Ayrshire Maternity Unit at the hospital, the health board said.
June and Fraser Morton’s son Lucas died at Crosshouse last November.
Mr Morton told the BBC: “Everything that could have gone wrong, went wrong. I believe they were understaffed and overworked. They didn’t have the training knowledge and experience, and I believe that comes back to management issues.
“If mistakes had not been made, the difference is quite simple. Lucas would have been here. It would have been his first birthday. The independent reports substantiate that and say earlier intervention would have led to a different result.”
Denise and Steven Campbell’s son Joseph died during childbirth at the same hospital four years ago.
Mrs Campbell told the broadcaster: “Our side of the story never, ever got asked. They said they just sat round the table with a cup of tea and talked about it and decided there was nothing that could have been done - that it was just one of these things.
“Then we spoke to the consultant who said things should have been done differently - especially in relation to monitoring Joseph’s heartbeat.”
The health board said it is engaged with both families and it has apologised to them.
Dr Alison Graham, executive medical director, said: “While we are unable to make any comment on these two cases, I would offer my assurance that we absolutely take these matters seriously. We are engaged with both families and will continue to engage with them about their concerns.
“I would take this opportunity again to apologise to both families for any failings they experienced during their time with us.
“NHS Ayrshire and Arran is committed to ensuring that if there is any possibility that there has been avoidable harm, this is investigated thoroughly and that we are open, honest and transparent about this.
“When reviews identify that there has been avoidable harm we speak with people affected and report this openly through our clinical governance systems. We also share any findings with the families concerned. This ensures we have the proper procedures in place to learn and improve.”
She added: “Since 2008 up until March 31 2016, there have been four Significant Adverse Event Reviews concerning stillbirth deaths at Ayrshire Maternity Unit. During this time, 33,716 babies have been born at Ayrshire Maternity Unit.”
She confirmed all midwives within the unit who are required to interpret cardiotocography results have completed annual mandatory training and do so every year.
Lucas’s death has been reported to the Crown Office, which is investigating.
A Crown Office spokesman said: “The investigation, under the direction of Scottish Fatalities Investigation Unit, is ongoing and the family will continue to be kept updated.”
“We’re committed to improving the Type 45’s power and propulsion system through a series of machinery upgrades during planned maintenance, and this work is progressing well.”