"Here we are, we're still going through the journey," Kathie told CBS News contributing medical correspondent Dr. Sanjay Gupta.
It's been a difficult journey for Naomi's twin brother, Caldwell. He's had three operations and remains in a neo natal intensive care unit. Kathie and her husband Whit believe that giving him breast milk, even through a feeding tube, is helping him recover.
"You can't be there all the time so it was my way to be able to be there for them all the time," Kathy said. "I'm providing for them."
Kathie is part of a new program at UC San Diego Medical Center that encourages mothers of premature babies, even babies who can't swallow, to commit to breastfeeding rather than formula. It's not easy.
"It's hard for them," said Dr. Lisa Stellwagen. "They're sick, they're tired, they're often afraid their baby isn't going to survive."
Only 45 percent of preemies go home on breast milk as compared to 74 percent of full-term babies. Doctors here believe that for babies born weighing only a few ounces, human milk means the difference between life and death.
"The premature infant is experiencing one of the worst nutritional crises in their life," said Dr. Jae Kim.
It's a crisis on two fronts. These tiny babies expend huge amounts of energy fighting life-threatening illnesses while at the same time doctors are desperate for them to gain weight.
"If we were trying to put on the same amount of growth as the smallest premature infants that we're dealing with, it would be something on the order of two or three pounds per day," Dr, Kim said.
Mother's milk may be as important as all the technology in the NICU.
"We're just starting to discover the power of what's in human milk," Dr. Kim said.
So it's good for babies, that's understood. But there's still some mysteries here. For one, not all breast milk is identical, even if that breast milk comes from the same mother.
So part of the program here involves analyzing the nutritional value of each mother's milk - and the results have been surprising.
"We're seeing a lot of variation based on whether she pumps in the morning, or at night, or depending on the day she pumps, we're seeing a 20-30 percent difference in her samples," said Dr. Charles Sauer. "For a preterm baby that can be a big difference."
One huge difference the program has made is a significant decrease in one life-threatening complication of prematurity - a gastrointestinal infection called necrotizing enterocolitis, or NEC. Of the half million premature babies born every year, between 5-10 percent of them develop it and a third of those die.
Before this program started, the rate of NEC in this hospital was 5.8 percent; last year it was less than 1 percent.
"The more human milk they're exposed to, the more reduction in complications such as necrotizing enterocolitis," Dr. Kim said.
Meanwhile, the Robinsons continue to bring breast milk to Caldwell, believing that it will help get him home sooner.
"If there's anything a mother can give to her children it's the nutrition, and support to help them grow and develop," Kathie said. "It just brings everything full circle."
Update: Katie Couric reports that Caldwell has just come home from the hospital, and we are told he and his twin sister Naomi are doing well.