The Bee Gees singer is currently at a private clinic in London after developing the illness, weeks after revealing he was beating cancer.
His brother Barry Gibb is said to have flown over from Tennessee, US to join Robin and other family members at his bedside, reports The Sun.
A family friend said: "They fear it may be the last time they'll see Robin. His recovery and determination has been remarkable, but there's been a turn for the worse.
"His body's taken a hell of a beating. The doctors fear for him but he's determined to battle on."
Robin underwent surgery to remove a potentially life-threatening blood clot at the end of March.
The singer's health issues started in October 2011 when he suffered from a twisted bowel, the same condition that killed his brother Maurice Gibb in 2003.
Barry's son Stephen also flew in to visit Robin from Miami yesterday (April 7).
> Robin Gibb: 'Cancer is payback for Bee Gees success'
Listen to Robin Gibb's song 'Don't Cry Alone' below: