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A medical mystery is deepening in California, where state health officials now say reports of polio-like illnesses that have left as many as 25 children with paralyzed limbs don’t appear to be connected.

It’s not clear what may be behind the rash of acute infections first reported Sunday by researchers in a presentation for the American Academy of Neurology's annual meeting. Tests of 15 of 20 cases submitted by doctors and researchers have come up empty, according to Dr. Gil Chavez, state epidemiologist for the California Department of Public Health.

“Thus far, the department has not identified any common causes to suggest that the cases are linked,” he said in a statement. “The investigation is ongoing.”

But that only heightened the resolve of the parents of 4-year-old Sofia Jarvis, who was the first to be identified as part of the series of unexplained cases of sudden paralysis in kids ages 2 to 16.

“Thus far, the department has not identified any common causes to suggest that the cases are linked."

She was barely a toddler two years ago when she was stricken with flu-like symptoms and trouble breathing — and later realized she couldn’t move her left arm. An MRI later confirmed that she had a spinal cord lesion that was causing paralysis.

"I'd like to say that Sofia is still a healthy young girl who's thriving," Sofia's mother, Jessica Tomei, 37, said at a news conference Monday. "She goes to pre-school. She does dance. We were very lucky that it only affected her left arm. But it's taken us a long time to get to that point to be OK with that."

Sofia’s parents joined doctors from Stanford University’s Lucile Packard Children’s Hospital to discuss the very rare — but very frightening — infections.

"This is a decision to let everyone know what happened to our daughter so that we can raise awareness and hopefully if there is anyone else out there, this will help them in the future," she said.

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Early surveillance identified five children between August 2012 and July 2013, but as many as 20 more cases have been identified since last summer, said Dr. Keith Van Haren, a pediatric neurologist at the hospital.

“We’re seeing them throughout California,” he said. “The farthest north is in the Bay Area and the farthest south is in San Diego.”

Van Haren and colleagues from the University of California, San Francisco, suspect that the illnesses may be caused by a virus, possibly a type of enterovirus, the same family of virses as poliovirus.

Two of the children in the early reports showed signs of infection with human enterovirus-68, which has previously been associated with polio-like symptoms. HEV-68 is a rare form of very common enteroviruses, which cause between 10 million and 15 million infections in the U.S. every year, according to the Centers for Disease Control and Prevention.

Other enteroviruses have been responsible for outbreaks elsewhere in the world, including Australia and Asia.

Like polio infections, most enterovirus cases cause no symptoms or only mild symptoms, but a fraction of cases can result in serious illness — including paralysis.

At its peak in the 1950s, polio paralyzed up to 20,000 people a year in the U.S., mostly children, until a vaccine eradicated the disease in the U.S. and virtually worldwide.

All of the children identified in the cases so far were immunized against polio. Although they were treated, recovery has been minimal at best, doctors said.

Identifying a common cause for the illnesses will be difficult, Van Haren conceded.

“The tricky thing for this is the window of opportunity for detecting the virus is very limited,” he said.

Spinal fluid samples would yield best results, but only for a couple of days. The virus could be detected in the nose and throat or in stool samples for longer, but those tests are much less sensitive and could lead to high numbers of false results.

“The tricky thing for this is the window of opportunity for detecting the virus is very limited,” Van Haren said. “We’re talking about doing a sort of epidemiological math where the scientists have to factor in how specific this is."

Van Haren and other researchers say they’ll work with state officials to collect and analyze information about new cases. They say that if children show signs of sudden limb weakness, with or without other illness, parents should seek medical care.

He cautioned parents not to panic.

“We want to temper the concern because, at the moment, it does not appear to represent a major epidemic,” Van Haren said. “The CDPH is taking these reports very seriously. We hope our efforts will help us develop prevention and treatment strategies in the future.”

NBC's Miguel Almaguer and Hayley Goldbach contributed to this story.