On Thursday, the actual due date, doctors held a news conference to update the public on her health. They are preparing to send her home by New Year's.
Weighing only 9.5 ounces at birth, Melinda was believed to be the second smallest baby to survive in the U.S. and the third smallest in the world.
"I've been here for 25 years. This is the smallest baby I've ever had to take care of," said Dr. Rangasamy Ramanathan, NICU Chief at County-USC Medical Center.
Melinda has been in the neonatal intensive care unit at County-USC Medical Center since she was born nearly four months early.
"The chances of living was like 1 percent. So out of that percent, we got her, it's a miracle," said her father, Yovani Guido.
Doctors warned her parents that babies born that premature often have developmental delays and can end up blind, deaf or suffering from cerebral palsy. But so far, Melinda is beating the odds. She now weighs 4 pounds - nearly eight times bigger than when she was born.
"Everybody thought that she wasn't going to make it at all. They doubted her, but she has made it through a lot. She's been through a lot, and so far, she's doing great," said her mother, Haydee Ibarra.
Melinda's doctor is quick to add that his smallest patient could still run into health problems. Preemies of this magnitude often have vision or hearing problems and learning disabilities. But it's hard to give concrete facts, he says, because babies this small are so rare.
"The first few days, it's just every minute. We were not sure if the baby was going to make it," Ramanathan said. "So far, the numbers look very good. But again, it's too early to tell how well the baby is going to do."
Doctors say 10 babies weighing less than a pound were born last year, and all survived. Doctors say another preemie was born just this week at County-USC, weighing exactly the same weight as Melinda. A tiny boy this time - who'd do well to look to Melinda for inspiration.
"She's a fighter. No doubt about that," Guido said. "She's a fighter."