Kate continues to struggle with the "effects of Hyperemesis Gravidarum," her spokesman says, and will not travel "on the advice" of her doctors.
She and William, both 32, met with doctors Wednesday and spent the evening considering the decision. Kate was given as long as possible to feel well enough to fly to the Mediterranean island, as she was eager to go and represent Queen Elizabeth.
It was going to be a milestone of sorts for her, as it would have been her first solo foreign visit.
William is said to be "honored" to be going for the weekend of celebrations marking the island nation's 50th anniversary of independence from Britain.
Palace sources say that when the HG struck, it was just as severe as when Kate was pregnant with Prince George in 2012 – and led to her being admitted to the hospital for a few days.
Fellow sufferers say the emotions of being pregnant can be "bittersweet." Caitlin Dean of the charity Pregnancy Sickness Support, who has suffered from the condition with each of her three pregnancies, said it's "really, really hard. You're happy to be pregnant, but at the same time you know you've got weeks or months of sickness ahead of you. It's really bittersweet."
The prince is set to start work soon on training for his job in the air ambulance service, beginning with theory, which will lead up to his exams.