The 62-year-old singer's wife Dwina, brother Barry, 65, daughter Melissa, 37, and sons Spencer, 39, and Robin-John, 29, have remained at his bedside in a private hospital in Chelsea, West London, according to the British news outlet.
Earlier this week, due to his ailing health, Robin was forced to cancel an appearance at the premiere of Titanic Requiem, his new classical work to commemorate the 100th anniversary of the ship's sinking.
In 2010, Robin had emergency surgery for a blocked bowel and then had an additional operation for a twisted bowel, his rep confirmed to CNN Saturday. He also had intestinal surgery on March 26 to remove a "blood clot that caused perforation."
In January 2012, Gibb opened up about his health struggles, telling The Daily Mail: "For more than 18 months, I had lived with an inflammation of the colon; then I was diagnosed with colon cancer, which spread to the liver. I have undergone chemotherapy, however, and the results -- to quote my doctor -- have been 'spectacular.' It's taken a toll, naturally, but the strange thing is that I've never felt seriously ill. I've mostly felt great."
Robin's twin brother, Maurice, died in 2003 at the age of 53 due to complications from a twisted intestine. His younger brother, Andy, died in 1988 at age 30 of a heart ailment.
"I sometimes wonder if all the tragedies my family has suffered -- like Andy and Maurice dying so young and everything that's happened to me recently -- is a kind of karmic price we are paying for all the fame and fortune we've had," Robin told The Sun in March, adding that he "can't wait to carry on with my work. I want all my fans to know their love helps me so much."
The Bee Gees' soundtrack to the film Saturday Night Fever was one of the best-selling albums of the 1970s. They have won seven Grammy Awards and were inducted into the Rock and Roll Hall of Fame in 1997.