The NSPCC has launched a campaign aimed at supporting parents like Anne and David.
Seven-month-old Jason had been crying almost continuously for several days - his parents, David and Anne, had not slept for most of that time.
They were exhausted and short-tempered - whatever they did to try and pacify Jason he just seemed to get worse.
One evening Jason woke screaming - Anne tried feeding him, but when he began to get hysterical she left him in David's care.
And David just snapped. He says he only shook Jason briefly, but before long the baby went limp and his eyes started rolling.
By the time they got him to hospital, he was bleeding in the brain and eyes.
This story has a happy ending - the baby recovered, the couple were assessed by the National Society for the Prevention of Cruelty to Children, undertook extensive counselling and eventually, when it was deemed safe, the baby was returned to their care.
But not all stories end as well as this. Infants under 12 months are four times more likely to be murdered than the rest of the population, with at least one killed every fortnight, according to Home Office figures.
A study published in the British Medical Journal found that up to three-quarters of babies under two taken to hospital with shaking injuries suffer profound disabilities or die as a result.
The NSPCC has launched a campaign aimed at supporting parents like Anne and David.
The point the charity is attempting to make, is not that these are bad parents, but that any new parent, faced with a baby that never stops screaming, can come close to the edge - and what's important is not to cross that line.
NSPCC director, Jim Harding, says: "The message is never hit or shake or treat your baby roughly because if you do you can turn understandable annoyance and anger into tragedy."
Chronic stress caused by sleep deprivation is likely, in particular, to exacerbate any post-natal depression, which in itself, severely strains the relationship between mother and child.
Julie Sait, from Norfolk, did not harm her baby, but in her depressed state following the birth she came close. Her reaction was simply to ignore her little boy.
"I found his crying very difficult to handle and left him with other people as much as possible," she said.
"I'd walk away and shut the door because I was frightened I would harm him."
The NSPCC also wants better ante-natal advice for new parents to help them cope, and education about family life in the national school curriculum.
The government has welcomed the latter idea and says parenting classes are going to be an integral part of the new guidelines on personal, social and health education in schools, due to be introduced in the next year or two.
The NSPCC campaign features a series of TV adverts, and there will also be a million leaflets in magazines, doctor's surgeries and toy shops offering advice to parents on how to protect their babies.
Names have been changed to protect identity