Dwina Gibb, who has been married to the Bee Gees star for 28 years, told The Sun that he refused to give up on the possibility of survival.
> Robin Gibb: 'Cancer is payback for Bee Gees' success
Robin slipped into a coma as he continued to battle colon and liver cancer and pneumonia.
He was on a ventilator for 12 days before emerging from the coma on Saturday (April 21).
Dwina told The Sun: "The doctors asked Robin if he wanted them to do everything in their power to save his life - or if he felt the time would come when enough was enough.
"He told them, 'There will never be a time when enough is enough. I want to live no matter what'."
> Bee Gees' Barry Gibb singing to brother Robin Gibb at hospital bedside
Despite the grim odds doctors gave the family on Robin emerging from his coma, he is now reportedly sitting up, breathing without the aid of an oxygen mask, and reportedly keen to make a musical comeback.
Dwina went on to discuss the premiere of her husband's classical work Titanic Requiem, which she and her son Robin-John attended on April 10 while Robin was in hospital.
She recalled: "The day before the concert it suddenly struck me that, instead of singing the beautiful song 'Don't Cry Alone' that evening, Robin was in a coma and might die... I couldn't bear it if his beautiful voice was silenced for ever."
Dwina went on to describe the bedside vigil the family had kept while Robin was unconscious, saying: "Barry sang a song he had composed for Robin. We played him Bee Gees music - and each time we did, tears began trickling down his cheeks.
> Robin Gibb 'made list of ambitions before coma'
"As we played him his song 'I Started A Joke', he opened his mouth on cue to sing. The doctors know relatives of coma patients are always looking for hopeful signs. They told me it could just be an automatic response."
The family persuaded doctors to attach electrodes to Gibb's brain and monitor his reactions to the music as it played. He reportedly woke from his coma midway through the Titanic Requiem.
"The nurses and doctors were astounded. Robin's voice, although a bit husky, is almost back to normal," Dwina added.
"We have to take each day as it comes. Robin has been seriously ill. Every time I go to hospital to see him, I am so happy to be there, so happy to see him with his eyes open and talking."
Listen to Robin Gibb's track 'Don't Cry Alone' below: