But older parents like the Plashas, who have been married 13 years, said their age had been a "huge advantage," in raising their son. "We had eight or nine years under our belt and had worked though a lot of things."
Mike Plasha, who had five children from a previous marriage before he was 30, said he is a better parent today at 55 than he was in his 20s.
"With Saul, I am more grounded, less uptight and am enjoying him tremendously," he said.
According to the National Center for Health Statistics, births to older parents, in the 45 to 49 age group, are on the rise.
But even though more Americans are having children later, adoption agencies say concerns about the longevity and energy of the parents dictate their rules.
And, they say, it is difficult to convince birth mothers to agree to older adoptive parents.
Iris, who did not want to use her real name, lives in a dorm at the oldest and largest institution, the Gladney Center for Adoption in Fort Worth, Texas. She will give up her baby for adoption when she gives birth in September.
"I feel that a parent needs to devote at least 20 years of their life to a child," said the unmarried 19-year old. "I don't want to judge, but 60 is too old. By the time the child is my age, they would be 80."
"I think younger is better, but not too young," she told ABCNews.com. "The age range is when you are most able to give up yourself to your child."
At Gladney, which handled 160 domestic and 300 international adoptions last year, the cutoff for parental age is 45 for the newborn program.
"Birth mothers are looking for a family that is young and will be able to provide a lifetime for their children," said Gladney spokeswoman Jennifer Lanter.
"The whole institution serves the best interest of the child, and obviously adoption agencies are geared toward securing a happy, comfortable, safe environment for the child. Older parents put that in more jeopardy."
But Dr. Richard Paulson, director of the fertility program at University of Southern California, said women as old as 50 -- and under some "extenuating circumstances," 54, should have the right to have children by any means if they are medically healthy.
"The thing we worry about most is whether the baby will make it to term safely," he told ABCNews.com. Mothers past the age of 55 are at greater risk of pregnancy complications that would cause a premature birth.
He requires his single patients to choose a co-parent before agreeing to assisted reproduction -- "a boyfriend, girlfriend or even a neighbor" who is willing to help raise a child in the event of the death of an older parent.
But beyond medical safety, Paulson sees no reason to regulate the age of a mother.
"Children are orphaned every day in this country, and even younger moms can be run over by a bus," he said. "They can get cancer or another disease."
"I think in this country, the respect for privacy and reproductive freedom is very high," said Paulson. "I am not saying it trumps the rights of the child, but most of think that a woman should be able to choose whether to carry a pregnancy or not," he said.
In 1997, one of his patients, Arceli Keh, lied about her age and gave birth to a baby at 63. The mother is still alive and her baby is now 12, according to Paulson.