HOUSTON — The baby’s lips were turning blue from lack of oxygen in the blood when his mother, Kristin Johnson, rushed him to an emergency room here last month. Only after he was admitted to intensive care with a respiratory virus did Ms. Johnson learn that he had been dropped from Medicaid coverage.

The 9-month-old, Elijah, had joined a growing number of children around the country with no health insurance, a trend that new Census Bureau data suggests is most pronounced in Texas and a handful of other states. Two of Elijah’s older siblings lost Medicaid coverage two years ago for reasons Ms. Johnson never understood, and she got so stymied trying to prove their eligibility that she gave up.

“I’ve been on this emotional roller coaster,” Ms. Johnson, 34, said of Elijah’s loss of coverage, an error that happened apparently because she didn’t respond quickly enough to a letter asking for new proof of income. “It’s been a very scary month.”

Nationwide, more than a million children disappeared from the rolls of the two main state-federal health programs for lower-income children, Medicaid and the Children’s Health Insurance Program, between December 2017 and June, the most recent month with complete data.

Some state and federal officials have portrayed the drop — 3 percent of enrolled children — as a success story, arguing that more Americans are getting coverage from employers in an improving economy. But there is growing evidence that administrative changes aimed at fighting fraud and waste — and rising fears of deportation in immigrant communities — are pushing large numbers of children out of the programs, and that many of them are now going without coverage. The declines are concentrated in a minority of states; in other places, public coverage has actually increased.

An analysis of new census data by The New York Times shows the number of children in the United States without any kind of insurance rose by more than 400,000 between 2016 and 2018 after decades of progress toward universal coverage for children.

Some of the states that saw the largest increases in uninsured children — like Tennessee and Texas — were those that created rules to check the eligibility of families more frequently or that reset their lists with new computer systems. In some states with large immigrant populations like Florida, doctors and patient advocates report growing concern among parents that signing up their children (who are citizens) may hurt their own chances of getting a green card or increase their risk of deportation.

When asked about the drop in Medicaid enrollment, government officials tend to point first to the improved economy, which has undoubtedly enabled some families to gain jobs with private insurance.

“Unemployment remains low, wage growth is up, & we now see fewer people relying on public assistance,” Seema Verma, the administrator of the Centers for Medicare and Medicaid Services, wrote on Twitter in April. “That’s something to celebrate.”

In many states with large declines, like Tennessee and Missouri, officials cited the stronger job market.

Kelli Weldon, a spokeswoman for the Texas Health and Human Services Commission, cited “record-low employment levels” for its contraction in Medicaid enrollment.

But the census analysis also shows increases in the rate of uninsured children in states with enrollment declines, including Tennessee, Texas, Idaho and Utah.

In Texas, the number of uninsured children rose by around 120,000 between 2016 and 2018. State officials increased paperwork requirements in 2014 for families covered under both Medicaid and CHIP, which serves children whose income is slightly higher than Medicaid’s.

Instead of checking eligibility once a year, as many states do, Texas enrolls children for six months and then checks databases for four consecutive months to ensure family income is still low enough to qualify. If the databases show the income has gone over the limit, families are notified by mail and have 10 days to prove otherwise or lose Medicaid.

A bipartisan bill in the state legislature this spring sought to make income checks annual again after data suggested several thousand eligible children were being dropped from Medicaid each month, but it never got a vote.

Other states have also begun checking family incomes more often, or removing families who may have moved if mail is returned to the state.

“The way they are doing this seems clearly designed to throw people off this program,” said Eliot Fishman, a senior director at the consumer group Families USA, who was a top Medicaid official in the Obama administration.

When Tennessee updated its enrollment computer system in 2016, it generated thousands of errors. Medicaid and CHIP enrollment in the state has declined by more than 55,000 children since January 2018, according to the Georgetown Center for Children and Families.

Tennessee’s Medicaid director, Gabe Roberts, said that besides the improved economy, the decline in enrollment was a result of updating the computer system and clearing up a backlog of old cases.

Gordon Bonnyman, co-founder of the Tennessee Justice Center, which has been helping families struggling with lost coverage, was skeptical, saying the state response has revealed “a remarkable lack of curiosity about what happened to these kids.”

The census shows that about 25,000 more children there have become uninsured since 2016.

A large body of evidence shows that Medicaid coverage for children has lasting effects on their lives, improving their health, educational attainment and even adult earnings. In 2010, the Affordable Care Act made it easier for states to check whether families qualified for Medicaid without requiring them to fill out paperwork, a strategy proven to increase coverage rates. The A.C.A. also made it harder for states to expel poor families for paperwork errors.

The changes helped the uninsured rate among children reach its lowest level ever in 2016, with fewer than 5 percent without coverage.

Trump administration officials have not explicitly tried to limit children’s Medicaid coverage. But Ms. Verma has repeatedly encouraged state officials to safeguard “program integrity,” by doing more vigorous checks of enrollees’ eligibility. More recently, her office reviewed the reductions and concluded that problems with state computer systems may be a factor in some places.

“While the economy is the most consistent driver of enrollment that we observed, we have found evidence that other more state-specific factors may be driving individual state experiences,” an agency spokesman, Johnathan Monroe, said in an email.

Medicaid and CHIP eligibility does depend on household income, meaning that, as wages rise, some families may be earning too much to qualify. Yet the patterns in coverage suggest reasons beyond improved finances. In Tennessee, for example, the biggest declines in Medicaid enrollment have come in counties with the highest unemployment rates, a Justice Center analysis found.

History has shown that when states require more paperwork from Medicaid beneficiaries, more eligible people fall through the cracks. Medicaid beneficiaries tend to move often; to have unstable hours and incomes; and to have literacy challenges that can make it hard to submit detailed renewal packages or verify their incomes frequently.

The specter of a pending “public charge” rule — which could penalize green card applicants who use public benefits like Medicaid — is causing many immigrant patients to decline enrollment, according to a Kaiser Family Foundation survey of community health centers. This month a federal judge temporarily blocked that rule from taking effect.

Texas leads the nation in the number of uninsured children and adults. In Houston, Maricela, a single mother, had carefully filled out the paperwork to re-enroll her younger two children, both citizens, in Medicaid every year since they were born — until now. A permanent resident from El Salvador who earns minimum wage as a hotel maintenance worker, she was so worried about jeopardizing her status that she decided to let their coverage lapse in August. Because of the deportation risk, she agreed to share only her first name.

“My worst fear is that I could end up without my legal status and be separated from my children,” Maricela said this month at Epiphany Community Health Services, a nonprofit group that helps people find health coverage. “That would be fatal for me.”

Her older son, 11, has asthma; at his last doctor’s visit before his coverage ended, she pleaded for extra medicine. His main treatment, a generic version of Singulair, could cost $150 a month without insurance. Listening to him cough at night, she finally decided to take the risk and re-enroll both boys in Medicaid.

“I had to do it,” she said. “But I’m afraid.”

Dr. Sogol Pahlavan, a Houston pediatrician, said the rate of her patients on Medicaid dropped to 70 percent in 2018, from 75 percent a year earlier. The number of uninsured in her practice of 10,000 patients has grown commensurately, with families citing both the impending public charge rule and administrative hurdles.

“It’s definitely going to affect the community, because somebody ultimately has to bear that cost,” she said. “These kids are still here; their chronic disease isn’t going away just because they’re losing health coverage.”

For Ms. Johnson, Elijah’s stay at Texas Children’s Hospital led to an appointment with an enrollment counselor who helped her try to figure out what had happened. Trying to re-enroll her older children earlier this year, she was asked for proof of income and missed the 10-day window to provide it; that may be why Texas dropped Elijah from Medicaid even though he qualified because he was a baby.

All of her children are now re-enrolled. But she has started receiving thousands of dollars in bills from the baby’s hospital stay — bills she is counting on Medicaid to cover retroactively. And she is haunted by what might have happened if the hospital where she took Elijah had considered the case nonurgent and turned them away.

“I went to the E.R. thinking he had insurance,” she said. “If the receptionist had not seen him turning blue, she might have just said, ‘He’s not covered, so we can’t see him today.’ I do think about that.”

Abby Goodnough reported from Houston, and Margot Sanger-Katz from Washington. Josh Katz contributed research from New York.

Abby Goodnough is a national health care correspondent. She has also served as bureau chief in Miami and Boston, and covered education and politics in New York City. She joined The Times in 1993. @abbygoodnough

Margot Sanger-Katz is a domestic correspondent and writes about health care for The Upshot. She was previously a reporter at National Journal and The Concord Monitor and an editor at Legal Affairs and the Yale Alumni Magazine. @sangerkatz • Facebook

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