They also made clear that her first solo foreign visit to Malta on behalf of the Queen next weekend was very much in jeopardy.
'The Duchess's attendance on the forthcoming visit to Malta will be kept under review and a decision taken closer to the time,' they said.
Kate is believed to be around seven weeks pregnant with her second baby but has sadly been hit by the same severe vomiting condition that blighted her first.
A source told Mail Online: 'If she continues to be as sick as she has been in recent days then all bets are off as regards her royal duties.'
She is suffering from hyperemesis gravidarum, which she experienced during the early stages of her first pregnancy.
Advice: David Beckham, who has known William for a number of years, has advised the couple to 'get more sleep' before the birth of their second child
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Advice: David Beckham, who has known William for a number of years, has advised the couple to 'get more sleep' before the birth of their second child
The condition, which affects 3.5 per 1,000 pregnancies, causes severe vomiting and can lead to dehydration, weight loss and a build-up of toxins in the blood or urine, called ketosis.
It is thought her illness began sometime last week and when William visited Oxford University on Monday without his wife to open the institution's new China Centre, he said the Duchess had experienced a 'tricky few days'.
David Beckham today offered his words of advice to William and Kate - get more sleep before their second baby arrives.
As the father of four children, the former England footballer is speaking from experience and reacted to news of the royal pregnancy by praising the couple's parenting skills.
Speaking during an interview with ITV's Lorraine show, Beckham gave the couple some words of wisdom: 'Get some sleep because jumping from one child to two is a big step even though I thought jumping from two to three was bigger.'
The former England midfielder was interviewed at New York fashion week where he is promoting his new collection for the brand Belstaff.
Beckham has known William for a number of years having joined forces with him to promote England's bid to host the 2018 World Cup, launched wildlife conservation campaigns with the Duke and been a guest at his wedding.
The sportsman added: 'But I'm so happy for them both because they're such great parents and obviously to be great parents and to have the roles that they have, as important as they have, is really incredible and I'm just happy that they're going to have another little one running around the house.'
The Prince of Wales greeted the news that he is to become a grandfather for a second time with joy and said he hoped the baby was a girl.
Yesterday, during a visit to the studio of a young entrepreneur who has been helped by his Prince's Trust said he would like a granddaughter.
As he left the premises in Bermondsey, South London he met Corey Johnson who congratulated him on becoming a grandfather for the second time.
The heir to the throne replied: 'I am already. But it's wonderful to be a grandfather again. I'm looking forward to it - but I hope it will be a girl this time.'
- Daily Mail UK
