Kaylee Wallace suffers from a rare brain abnormality that could cause her to stop breathing, but she continued to do so after she was removed from a respirator on Tuesday. (Family photo/Canadian Press)

The parents of a gravely ill baby girl who had offered her heart to save the life of another seriously ill infant were told by doctors Wednesday afternoon that their daughter's condition was stable for the time being but that she could still die.

"This is a moment-by-moment, hour-by-hour situation with our daughter's stability — no doubt," Jason Wallace told reporters after consulting with doctors at Toronto Hospital for Sick Children about his two-month-old daughter, Kaylee Wallace.

Lily O'Connor is in intensive care after a planned heart transplant was called off. (Family photo)

"These doctors are still not willing, obviously, to say she's going to live. They're still willing to say that she has profound spells that could take her life instantly."

Wallace said he was told the condition of Kaylee's heart is "fine" and that he, his wife and doctors will revisit the organ donor issue if and when the time comes.

"There's a standby order that if she went to that stage, we will go back to that if it's necessary," he said. "It'll be a decision made at that moment, and we'll be here to make that decision."

Earlier Wednesday, hospital officials said Kaylee, who was believed to be terminally ill, was in stable condition.

She had been an organ donor candidate, but that was no longer the case after she exceeded doctors' expectations and survived being taken off a respirator on Tuesday night, they said.

Emotional roller coaster

Wallace told CBC News the experience has been an emotional roller coaster, and he said doctors have still not been able to give a prognosis.

Dr. Jim Wright, chief of surgery at Sick Kids, said Wednesday that Kaylee will continue to be treated at the hospital's intensive care unit.

"Certainly at this point, she is not a candidate for transplant," he said.

Kaylee, from Bradford, Ont., suffers from Joubert syndrome, an extremely rare brain abnormality that could cause her to stop breathing during sleep.

Wright said the condition comes in a variety of severities.

"It was believed that Kaylee had the most severe kind and she would not be able to breathe on her own," he said.

Kaylee was expected to die on Tuesday night, and surgical teams were on standby to perform a risky procedure known as death cardiac donation to harvest her heart and transplant it into one-month-old Lily O'Connor.

The operation was called off after Kaylee stayed awake during the one-hour window in the operating room.

'She's a fighter'

Wallace and Kaylee's mother, Crystal Vitelli, had come to terms with the idea her heart would live on in another baby and had said goodbye to their child.

Lily, the recipient, was born March 9 with truncus arteriosus, a rare form of congenital heart disease that leaves her blood short of oxygen.

On Saturday, Lily's parents, Kevin O'Connor and Melanie Bernard, thought they had found the miracle they were looking for when they were approached by Kaylee's parents at the hospital about a possible transplant.

Doctors at the hospital, however, initially downplayed the chances of a successful procedure, saying that when Kaylee was taken off life support, it would likely take her too long to die to make her heart useful for transplant.

Speaking to reporters as they entered the hospital on Wednesday, the P.E.I. couple said they were told Lily could live "weeks to months" without a transplant.

"It depends on how she is, and she's a fighter," her father said.