More than 70% of neonatal units in the UK have had to shut their doors to new admissions at some point in the last six months, a survey suggests.
The charity has launched a charter of healthcare rights for babies
Most said they had not been able to take any more sick and premature babies because they had had too few nurses.
Charity Bliss, which surveyed 153 units, found this led to many babies having to travel hundreds of miles for a cot, and called for more investment.
The Department of Health said it was considering the evidence from Bliss.
Bliss said putting in 2,700 additional nurses could save the lives of up to 500 babies a year.
The UK has some of the worst perinatal (up to seven days after birth) and infant mortality rates for Western Europe.
Death rates for babies and infants increased in 2003 for the first time in many years, from 5.2 deaths per 1,000 to 5.3 per 1,000.
Perinatal mortality figures for that year were the worst since 1996, at 8.5 per 1,000.
There are also wide variations in infant mortality rates across the country. In parts of Scotland, a baby is three times as likely to die before its first birthday than in the south of England.
Bliss says £75m would pay for the staff increase needed to give adequate care in neonatal care units, allowing those in intensive care to receive the same one-to-one nursing that children and adults are entitled to.
Only 2% of units currently achieve that standard, which is set down by the British Association of Perinatal Medicine.
Of the 153 units who responded to the survey - carried out by the National Perinatal Epidemiology Unit, on Bliss' behalf -72% said they had closed their doors to new admissions at least once in the preceding six months.
Bliss said one hospital, St Michael's in Bristol, had only been able to take new admissions on three days out of 30 in June this year.
A spokeswoman for the trust said it worked with other hospitals in the area so they could take referrals when it was full.
The Bliss survey found units did take babies where they could - 95% reported they had accepted more babies than they felt they should have done.
Rob Williams, chief executive of Bliss, said: "More and more babies are being born prematurely. Each year, more are surviving."
He said a baby born weighing 2lb (0.9kg) 20 years ago had a 20% chance of surviving, but that had now increased to 80%.
But Mr Williams added: "This report puts the spotlight on a health service that remains severely under-resourced even while other parts of the NHS are seeing big improvements."
Bliss has also launched a "bill of rights" for babies, outlining their right to high quality, sensitive care.
'More to do'
Professor Neil Marlow, of the British Association of Perinatal Medicine, said: "It is vital that neonatal services and the government continually review provision of care, so we can improve the outlook for these vulnerable infants.
"This report highlights some critical shortfalls that still need to be addressed."
A spokeswoman for the Department of Health said, while mothers and babies needed to be cared for as close to home as possible, some babies needed specialised care.
But she added: "There is clearly more to do."
She said the department would consider the evidence from Bliss to see where more could be achieved.
Shadow Health Secretary Andrew Lansley said: "It is vital we give paediatric services dedicated resources and structure to ensure service capacity, staffing and standards can be enhanced."