(ABC News) -- A couple from New York are pleading for the public's help to raise awareness and funds in order to find a cure after two of their children were diagnosed with a rare and fatal genetic disease.

"They're beautiful babies, they're happy babies," Gary Landsman told ABC News of his two sons. "Josh, at about 4 months now, is starting to smile and starting to become happier."

"Benny, at 17 months, should be doing more things, he should be crawling, he should be beginning to talk but he's not," he added. "But he's happy and smiling."

Gary Landsman and his wife, Jennie Landsman, told ABC News that they first became concerned when their older son, Benny, seemed to be developing motor skills at a slower pace than most infants.

"Around six months he wasn't holding his head up, and he wasn't sitting by himself, which he should have started to do independently at that point," Jennie Landsman said.

The couple took Benny to see countless specialists over the next few months, desperate for a diagnosis. Eventually, Jennie Landsman said that a geneticist told her that Benny was "missing an enzyme."

"I said, 'OK, when can we start giving it to them?' Like, it seemed so simple," she added. "And she said, 'No, it's fatal,' and just like that ... it was like the world ended."

The couple found out that Benny had Canavan disease, an extremely rare degenerative disorder. Canavan disease currently has no cure, and most children diagnosed with it do not live past 10 years old, according to the nonprofit advocacy group Canavan Foundation.

"Canavan disease is a rare genetic disease that affects the ability of the brain to send and receive messages," Dr. Joanne Stone, the director of maternal-fetal medicine at Mount Sinai Health System in New York City told ABC News.

At the same time that the Landsman family finally got a diagnosis for Benny, they had also just welcomed home their 2-week-old son Josh. The family was heartbroken to learn that Josh also tested positive for the Canavan disease.

"We're taking life day by day right now because when you think about the big picture, I don't want to go on," Gary Landsman told ABC News, "I don't."

Jennie Landsman added that they are coping with the double diagnosis "minute by minute."

Symptoms of Canavan disease begin appearing in children when they are between 3 and 5 months old, and the disease can affect a baby's ability to develop skills such as turning over, controlling head movement and sitting without support, according to the National Institutes of Health.

While the disease is extremely rare, it is most common in people of Eastern European Jewish descent, and it can be predicted by genetic testing. The disease affects approximately 1 in 6,400 to 13,500 people in the Ashkenazi Jewish population, according to the National Institutes of Health, although the frequency of the disease in other populations is currently unknown.