Rebecca Smith and Mark Barton - who also have a four-year-old daughter Amelia - fear further tragedies if immunisation is not rolled out beyond newborns.
They have even bravely shared a photograph of Duke hours from death, in a bid to show the reality of what meningitis did to their little boy.
They spoke out to encourage more people to sign a petition for the subject to be debated in Parliament.
But in response to the most signed petition in parliamentary history, the Department of Health said it was following the expert advice of its Joint Committee on Vaccination and Immunisation (JCVI).
It said it would not be cost effective for the NHS and would not represent a good use of NHS resources.
Rebecca, 22, said: “I would love them to reconsider, even if it was just to under fives to start with, at least it’s a start.
“I feel that the children who have died need a bit of justice.
“This is deadly and it seems to be occurring more and more often.”
Shortly after Duke’s death last year, the Government struck a deal for all babies to be given the potentially life-saving meningitis B vaccine free of charge.
Babies receive the first vaccine at two months old, followed by another at four months and a booster at 12 months.
Parents who wish to have older children vaccinated must pay privately - at up to £200 per child - but there is a worldwide shortage of the vaccine and stocks are low.
Rebecca added: “I got in touch with my GP to see if I could get Amelia vaccinated free-of-charge but I didn’t get very far, I think it depends which practice you’re at.
“But I feel when you’ve been through it and lost a child, you should be entitled to this. Surely they don’t want a family to lose another child?
“I haven’t taken Amelia to be vaccinated privately. Part of me thinks should I borrow the money and get it done?
“But then I think surely not, it won’t happen to us again, but then you never know.”
Hazel Maltby, a mum of four, also urged the Government to reconsider its policy, after her daughter Isla contracted meningitis at five weeks old.
She said the £800 cost of vaccinating all of her children was prohibitive, and was putting many families in an awkward position.
The 39-year-old said: “Isla had had a urine infection and then her temperature got to 41.2 degrees celsius, so we took her to hospital.
“The doctors were really reassuring and gave her a high-strength antibiotic, but when they mentioned meningitis, we couldn’t believe it.
“She was in the very early stages of it so wasn’t showing any of the symptoms, so we’re forever grateful she had the urine infection, that was a complete coincidence.
“Nothing really came of it and she’s six now and it’s had no lasting affects.”
She added: “I haven’t had mine privately immunised. At £200 each it’s an awful lot of money for any family. And when you’ve had one whose had it, you think what are the chances of another getting it?”
Mum-of-three Emma Williams, 26, wants the vaccine rolling out to all children, so other families don’t have to go though what hers did.
She was told son Jamie, now five, was “24 hours from death” when he was struck down with meningitis two years ago.
Emma said: “He started with a temperature and a tiny rash on his leg and within 24 hours he was fighting for his life. We were told to expect the worse. In the short time it had taken to get him to hospital, the rash had spread all over his body, the septacaemia had set in really bad.”
Emma said seeing a raft of pictures on social media of children suffering with meningitis has brought the horror back to her.
She said: “Seeing those pictures brought it all back - you don’t think it will happen to you. It was terrifying to see how poorly he was in such a short space of time.
“Jamie was transferred to Alder Hey and spent three-months in hospital. He was given blood tranfusions and skin grafts. There is the after affects too. He still requires treatment now.
“To think there is a jab to stop other families going through what we went through - it should be made available to everyone.”
Friend Lisa Ashcroft, 33, a mum-of-two said: “These cases reinforce how devastating meningitis can be. You shouldn’t have to put a cost or a cap on protecting your children.”
The Government statement in response to the petition said: “With this programme, our priority is to protect those children most at risk of Men B, in line with JCVI’s recommendation. The NHS budget is a finite resource. It is therefore essential that JCVI’s recommendations are underpinned by evidence of cost-effectiveness. Offering the vaccine outside of JCVI’s advice would not be cost effective, and would not therefore represent a good use of NHS resources which should be used to benefit the health and care of the most people possible.
“When any new immunisation programme is introduced, there has to be a cut-off date to determine eligibility.
“While this is extremely difficult for parents whose children aren’t eligible, there is no other way of establishing new programmes to target those at highest risk without introducing inequalities.”
• See https://petition.parliament.uk/petitions/108072