Prince Friso's doctors have said that he may never regain consciousness after being starved of oxygen for so long. The prince was skiing off-piste in the Lech resort with a childhood friend when the avalanche struck.
At the time the alert level was at the second highest, posing a particular risk away from the prepared ski slopes. The friend was carrying an avalanche "air bag" and escaped without serious injury, while Prince Friso was buried beneath a 100-foot-wide slab of snow and was only found with the help of a signalling device he was carrying.
It then took nearly 50 minutes to resuscitate the prince after he was pulled from the snow - time that may have caused permanent damage, said Dr. Wolfgang Koller, head of trauma at the Innsbruck hospital.
"It is clear that the oxygen starvation has caused massive brain damage to the patient," Dr Koller said. "At the moment, it cannot be predicted if he will ever regain consciousness."
Prince Friso was on Saturday still in a coma – a state of unconsciousness in which a person cannot be awakened by sound or touch. And the MRI scan which they performed on Thursday, six days after the accident, confirmed the family's worst fears.
"We had hoped that the slight cooling of the patient would protect his brain from too serious damage," said his doctor. "Unfortunately this hope was not fulfilled."
The Dutch media, usually low-key, has been swept up in a wave of emotion. Dutch journalists departed en masse to Lech when news of the accident broke and are still keeping vigil outside the hospital. Several television journalists, male and female, were in tears when reporting from Austria and scheduled television and radio programmes are being interrupted frequently with news and updates.
Ary Vander Waay, a Dutch supporter of the royal family, said: "If the prince dies – and we hope he will survive – you can expect emotional Princess Diana-like scenes in the Netherlands."
Prince Friso is easily the most popular of the three Dutch princes, although his elder brother Willem-Alexander is first in line to succeed the 74-year-old Queen Beatrix.
Academically he did better than both his brothers at the VCL school in The Hague. He excels at finance, working for a time for Goldman Sachs and handling the Dutch royal family's considerable fortune. He has also been chief financial officer for Urenco, a uranium enrichment company based in Berkshire.
Shying away from the limelight, Prince Friso moved from the Netherlands to London, installing his young family in the west London suburb of Kew. His daughters Luana, 6, and Zaria, 5, were thought to attend a local London school, and the prince rarely appeared in public in the Netherlands.
In 2004, when he married Mabel, he was forced to renounce his claim to the throne, owing to a Dutch law that states that royals need parliament's permission to marry – with the request submitted by the premier on behalf of the Dutch cabinet.
After it emerged that his future wife withheld details of her previous relationship with a Dutch drug baron, then prime minister Jan Peter Balkenende declined to ask parliamentary permission.
The prince nonetheless married his bride, taking the loss of the title in good humour, having always referred to himself as a "reserve pretender to the throne."
But to his family, he was indispensable. And they are now consulting with surgeons and specialists about how to proceed, and how to readjust to having their world turned upside down.
It is thought likely that he will be moved to a rehabilitation clinic – probably in the UK. Dutch sources told The Sunday Telegraph that should the royal family eventually have to make the painful decision to cut off his life support machine, it would be preferable if this did not take place in the Netherlands.
"Usually this kind of horrible decision can be made by a family in private. In the case of the Dutch royal family, they would of course be the focus of the public and the media – not a comfortable position," the source said.
Dr Andy Eynon, a consultant in neurosciences intensive care and the director of major trauma at Southampton Universities NHS Trust, said it was "routine" to transfer coma patients from an accident abroad back to their country of residence.
But he said it normally took months to determine how well a patient with a severe brain injury might recover.
"You can't say somebody is in a persistent vegetative state until six months after an injury involving lack of oxygen to the brain, or 12 months after a trauma injury to the brain.
"In the early stages, a week or so post-injury, it is very difficult to predict where on that spectrum the patient will be. Over the years we have been astonished at the number of people that can recover and regain very valuable lives. I have seen some people recover from extremely severe injuries."
But the Dutch royal family do not sound optimistic.
"At present it is not certain whether he will ever regain consciousness," they said in the statement. "In any event, rehabilitation will take months, if not years.
"We hoped that the patient's mild hypothermic state had sufficiently protected the brain against excessive damage. Unfortunately, our hope was in vain."