A new report says most neonatal units in the UK have had to shut their doors to new admissions at some point in recent months.
This has often led to babies being cared for many miles from home, premature baby charity Bliss says.
Sian Matthews-Tickner, of Lingfield, Surrey, has given birth to two premature babies.
Her first, Jake, was born at 34 weeks weighing 3lb (1.36kg) and was cared for at the family's local hospital in Wales, where they then lived.
Sian's second son Alfie, now 20 months old, was born at 25 weeks weighing just under 2lb (0.9kg).
Before his birth, Sian was transferred to a hospital in Chatham, Kent, 50 miles away from her home, which could offer the specialist care she needed.
But, while she was discharged a week after his birth, Alfie was kept in for 104 days, meaning the family had to travel to and from Chatham each day to see him.
Sian, 37, would travel up every morning, and be home in time to meet her son Jake from school.
Her husband Sean, a fireman, went to see him in the evening.
Sian says she calculated that the family travelled 7,000 miles to see Alfie over the three months he was in hospital.
She said: "It put horrendous pressure on the family.
"I always thought when people went through a trauma it brought them together.
"But during that time, we argued over the silliest things.
"It got to the point, when Alfie was three months old, where I was in tears and had to tell the nurses I couldn't afford to put petrol in the car to visit him the next day."
Staff at the hospital offered Sian money from a charity set up to help people in her situation, but Alfie was transferred to their local hospital, so the family had no need to use it.
"It was much better. I could be there all day. And my other son could come up and see his brother."
Alfie had a twin, who died in the womb - a fact that was not discovered until Sian gave birth and a second foetus was found.
The family now have to visit five hospitals regularly.
Jake has learning difficulties, due to being born prematurely, and also suffered a bowel infection at three months old which has had lasting effects.
Alfie is profoundly deaf and has branchiootorenal syndrome, a rare genetic disorder which leads to cysts and pits on the neck and in front of the ear.
He also has a chronic lung infection and asthma.
Sian said: "I always wanted lots of babies, and I wouldn't be without my sons. But I think we've decided no more now."