NEW YORK (CBSNewYork) — For one Long Island family, it’s a special holiday season.

Tyler Rappoport will turn one year old on Christmas Day.

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It’s a happy time, and one they once doubted they would ever see.

“The fact that we’re here today is unbelievable,” Tyler’s mother, Jacquleyen, told CBS2’s Cindy Hsu.

At first, life with Tyler was blissful.

“He was a happy baby and an easy baby, sleeping throughout the night, smiling early,” she said.

But at about three months, it all changed. Tyler became difficult to feed, he cried all the time and Jacquleyen said something seemed very wrong.

“I just knew deep down that this was not how it’s supposed to be. It’s not supposed to be this difficult,” she said.

Doctors told her not to worry.

“They told me I was a nervous mother. They would say this: ‘mom, babies cry,'” she said.

Doctors finally ordered tests, but just as they were about to be performed, Tyler suddenly went into cardiac arrest.

“I didn’t think that he was alive at that point,” Jacquleyen said in tears. “And I just kept asking them, ‘is he alive?'”

It turned out Tyler’s heart was failing and he would need a new one transplanted.

“I was so scared for my son’s life,” his father said.

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Pediatric Transplant Director Linda Addonizio said most babies who need new hearts die because there are so few donor hearts available.

“It sort of tears at you every day. You see the agony of the family, the child, the agony of all the caregivers,” she said.

As the days went by, Tyler grew sicker and sicker and went into cardiac arrest multiple times.

“He was at death’s door. He was there, he was there. They brought him back to life,” his mother said.

Finally, after two months, a donor heart was found.

“I was probably doing cartwheels through the hospital floor,” she said.

Their joy was tempered by a hard reality — that another family had lost a child that would save theirs.

“They must have had such incredible strength,” she said.

Helen Irving, the president of Live On New York, said such donor families have a unique perspective.

“If they can for a moment prevent another family from feeling that level of grief,” she said. “If one child dies, why does another child have to die?”

“We don’t know them, but they will forever be our heroes,” Jacquleyen said.

Now, Tyler is happy and healthy, and the Rappoports are counting their blessing this holiday season.

“It’s a true Christmas miracle,” Jacquleyen said.

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Columbia Presbyterian performs the most pediatric heart surgeries in New York with about 20 a year.