Renner, who wasn't expected to even enter the world alive, turns 2 on Friday.
During the pregnancy with their third child, Brian and his wife, Karen – the family lives in Sioux Falls, South Dakota – were told that he had a slew of medical complications, including Down syndrome and a condition known as hydrops fetalis, which causes fluid buildup in the body. The prognosis was dire.
"They told us that he was really likely to not be born alive," Karen, 38, tells PEOPLE. "But my husband and I decided to keep hope. We didn't get his nursery ready; that would have been too devastating. But I remember standing at the window, envisioning Renner playing in the tree house with his brother and sister. I'd also sing 'This Little Light of Mine.' I'd tell him, 'Come on, buddy, keep your little light shining.' "
As the pregnancy progressed, an echocardiogram revealed that the baby was experiencing reverse blood flow and his organs were failing. Karen was rushed to Sanford USD Medical Center for an emergency C-section.
Renner entered the world "looking like a little teddy bear," Brian, 36, recalls. "He had a whole head of black hair, a short stature and was swelled up."
"He took one breath of life, and that was really all we'd prayed for," Karen adds. "We prayed that he'd be born alive so we could meet him alive."
Courtesy Darla Atlas
"Some days we were taking it minute by minute," Karen says. "It was pure agony to see him that sick. You feel helpless as a parent. But you have to find the good in each and every day, no matter how hard that is."
In his dim hospital room – too much light caused Renner's blood pressure to skyrocket – his parents read him bedtime stories, brought in a radio that played nonstop country and Christian music, and held his tiny hand as often as possible.
When he was about 2½ months old, Renner's condition deteriorated further. He'd reached the maximum setting on his special ventilator, and doctors performed a medically induced paralysis to keep him alive. But they warned that the end was coming.
"They sat us down and told us that he's not going to survive – that it may be weeks or months, but he won't survive," Karen says.
When the doctor asked, "What do you want?" she replied, "I want to hold him."
Courtesy Darla Atlas
"Everybody thought that was a mom's last wish for her dying son," Karen says.
Against All OddsBut instead of dying, Renner began improving. Slowly but surely, "because of something inside of him, or something from above, everything just changed," Brian says.
"As he grew bigger and shed all of the support off him, a little person emerged through all of that hurt and pain he'd gone through," says Dr. M. Akram Khan, the neonatologist who delivered Renner. "He would look straight in your eyes and seemed to say, 'What was all the fuss for?'
"I was amazed by the speed he made recovering from what we all thought was dismal," Dr. Khan adds. "He is a miracle, and his hugs are to die for."
On Jan. 11, 2013 – 198 days after he was born – the Wollmans took Renner home.
"Every heartbeat is a heartbeat of gratitude for his medical team," Karen says. "I can never thank them enough."
Renner still deals with lingering complications in his lungs and has pulmonary hypertension, among other issues. But against all odds, the outlook for his future is good – which is great news for his adoring family.
When big brother Riley, 10, and 6-year-old sister Paisley come home from school, "the first thing is always, 'Where's Renner? Where's Renner?' " Brian says. "I don't get the first hug anymore – he does."
"Oh my gosh, he's awesome," Karen says of her youngest child. "We're enjoying each and every day he's here."