Read local coverage of this story at CNN affiliate WYFF.

(CNN) -- A baby boy is clinging to life at a South Carolina hospital, three days after being abandoned in an arena toilet after a circus show, police said.

A custodian discovered the infant, thought then just to be an hour or so old, late Friday night at Greenville's BI-LO Center. The boy was immediately brought for medical attention, with authorities unaware of how he'd gotten there or who his mother was.

Greenville Police Chief Terri Wilfong told HLN's Nancy Grace on Monday that authorities were sifting through videotape taken in and around a particular restroom, hoping to identify the woman who gave birth to the boy. Still, a single camera wasn't fixed on that site the entire night, she noted.

"The cameras do not stay stationary -- they move, so they do not have a constant vision of the bathroom," she said.

Several other factors are also complicating the search, including the possibility the mother may have taken pains to hide her pregnancy. Also, Wilfong noted, those attending Friday night's event may have come from anywhere.

"With 10,000 people (in the arena), it makes it very difficult," said Wilfong. "But we're doing everything we can."

This weekend, Greenville Police Sgt. Jason Rampey told reporters he didn't think "it's physically possible that a mother would not know (she) had given birth to a child."

He added, too, that it seems unlikely such a woman would be able to hide her pregnancy from everyone, pressing the public to reach out to police if they have ideas on who the mother might be.

"Somebody -- a parent, a family member or a friend -- would know that (she) was pregnant," Rampey said.

According to Rampey, a custodian found the newborn after the Ringling Brothers and Barnum & Bailey performance, after hearing "what he believed to be a child crying or whimpering."

The baby was in the toilet water and soon rushed to the Children's Hospital at Greenville Memorial Hospital to be treated for hypothermia, according to CNN affiliate WYFF.

Besides investigating possible criminal wrongdoing, related to abandoning a child, Rampey told reporters that police wanted to find the young mother to assure her own health and well-being.

"She would need medical attention at this point," he said.