A smile, a swallow or a step mean a lot to Rob Marianetti.

It was not long ago that his daughter was unresponsive, following a bathtime incident, and doctors told him there was no hope she would get better. But Marianetti isn’t giving up on Kayla, and coming up on her third birthday she can make some sounds and move her arms and legs.

“I’ve been on a mission to get my daughter back,” he said.

When she was 17 months old, while Marianetti was at work — for Setauket-based Hurricane Tree Experts — Kayla was having a bath in her Port Jefferson Station home and was left unattended for eight minutes, the father said. She was found floating and unresponsive.

Marianetti rushed to the hospital to see Kayla while doctors were working on her. He said he was trying to get into the room with her and was banging on a door to the point where a police officer had to intervene. He learned a few weeks later, he said, that his daughter came back to life while he was banging.

“She was blue and she was done. She was done — and she came back.”

Kayla spent time at St. Charles Hospital and Stony Brook University Hospital, and Marianetti and his wife — who is no longer “in the picture,” he said — got the little girl started on different therapies right away, so she would not deteriorate.

The whole time Kayla was in the hospital, Marianetti never left her side, the father’s aunt, Susan Calvi, said: “Slept there every day.”

Out of all the nation’s experts Marianetti saw, he said, just one, neurologist Dr. Chris Sinclair at John T. Mather Memorial Hospital, encouraged him to fight.

Sinclair said he’s seen a similar case of brain injury before, in which a child was perhaps even worse off than Kayla in the beginning but after a couple of years was walking and talking.

“So I’ve seen it before but I also know how flexible, in a sense, the brain of a young child is.”

Sinclair explained that there are connections between brain cells that allow the cells to communicate with one another, and in Kayla those have become damaged. But those connections can be regrown in a developing brain.

“When someone’s so young, [the future] is a lot brighter than it would be for someone who is an adult because the brain is still developing,” Sinclair said. “I think the sky’s the limit for her.”

Kayla has multiple therapy appointments each day, whether it’s hyperbaric therapy, which involves putting her in an oxygen-rich environment; physical therapy, to move her toward sitting up, standing and walking; vision therapy, as neurological issues have made her legally blind, even though her eyes themselves are fine; or speech therapy, which is used both to teach her to communicate and to eat on her own.

“By me doing all this stuff, it’s friggin’ working, man,” Marianetti said. Kayla has stood up, laughed, swallowed a small amount of pudding and taken a few steps. “Now remember, she couldn’t move a year ago. … I have hope.”

One big hurdle for Marianetti, however, is money. He’s gone through his savings, he said, and Kayla’s therapy appointments cost $8,000 a month. Then there’s other medical costs, as well as living expenses like food, diapers and electricity.

The treatments are expensive, the dad said, but “how can I not continue what I’m doing when she’s making progress?”

He set up a fundraising page, at www.gofundme.com/n19qgc, to ask for help. As of Wednesday morning, the fund had reached $18,000.

His goal is to have Kayla at least be able to walk, talk, eat and see on her own.

“I’m not leaving her like this,” Marianetti said. “I’m going until either she gets better or I die.”