Princess Margaret is in the care of specialists at a private London hospital where she is being fed through a tube.
Doctors are carrying out a thorough assessment of the Queen's 70-year-old sister.
She was admitted to the King Edward VII Hospital yesterday suffering a severe loss of appetite after a suspected second stroke just before Christmas.
Buckingham Palace said Margaret had spent a comfortable night and her condition was continuing to be assessed.
Her children, Viscount Linley and Lady Sarah Chatto, issued a joint statement thanking the Princess's friends and well-wishers for their kind messages.
Lady Sarah is expected to be at her mother's bedside. Lord Linley visited on Wednesday night.
Margaret was taken to hospital from Sandringham where she had been given special nursing care but failed to respond to treatment.
Her doctors had hoped the Princess would benefit from staying at the Queen's Norfolk estate and being with the Royal Family.
However, Margaret was eating so little she had to be admitted to hospital.
Lord Linley and Lady Sarah were said to be in close touch.