Abercrombie & Fitch announced last week that it would stop requiring workers to be on call for shifts that could be canceled with little notice, making it the latest retailer to pull back from such scheduling practices.

Williams-Sonoma ended on-call shifts in the last several months, while Gap has scaled back the practice ahead of a study it has commissioned on scheduling. Last year, Starbucks announced that it was bringing more “stability and consistency” to its employees’ hours after an article in The New York Times highlighted the company’s habit of giving workers little advance notice on their schedules and requiring some to close and open stores in consecutive shifts, known as “clopening.”

Although the workers directly affected by unpredictable schedules are the most obvious winners, the biggest beneficiaries of a change in the practice could be their children.

A growing body of research suggests that children’s language and problem-solving skills may suffer as a result of their parents’ problematic schedules, and that they may be more likely than other children to smoke and drink when they are older.

“Young children and adolescents of parents working unpredictable schedules or outside standard daytime working hours are more likely to have inferior cognitive and behavioral outcomes,” the Economic Policy Institute, a liberal advocacy group, said last week in a report.

Last year, two Democratic representatives introduced the Schedules That Work Act, which would require employers to give workers more say about their hours and provide them with incentives to encourage more stable schedules.

“We are all talking about this today,” said Representative Rosa DeLauro, Democrat of Connecticut, who is one of the bill’s lead sponsors. “Five years ago, it was an issue people would have brushed to the corner.” The bill has 69 co-sponsors; two Democrats also introduced companion legislation in the Senate.

Among the needs that policy makers and activists working on the issue identify is finding stable, professional child care on a schedule that shifts from week to week.

“The arrangements families put together are usually ad hoc,” Ms. DeLauro said. “They have to rely on other family members, friends. If something breaks down in that chain, they have a problem.”

While all shifting schedules pose a challenge in this regard, on-call work may be unique in the way it complicates child care arrangements.

Kris Buchmann of Albuquerque worked a retail job at a local mall when her son, now 3 ½, was about 1 year old. She said she was frequently scheduled for on-call shifts that never materialized or that lasted less than an hour when they did.

“I still had to pay a babysitter,” said Ms. Buchmann, who is active in a New Mexico organizing group called Organizers in the Land of Enchantment, or OLÉ. “Sometimes I would have to go pick her up, take her back to my house because she didn’t have transportation, drive to work, get sent home, still have to pay her, and drive her home.”

When Ms. Buchmann demanded a more stable schedule, her employer refused, an experience that is not uncommon. After that, she left the job.

As practices like unpredictable scheduling have proliferated in recent years, fed by a shift toward lean staffing models made possible by sophisticated software, they have attracted public criticism.

In a nationwide New York Times/CBS News poll in May, 72 percent of Americans favored requiring chain stores to provide at least two weeks’ notice for any change in schedule, or else compensate workers with extra pay.

Regulators have also taken notice. In April, the office of the New York State attorney general sent letters to 13 retailers, questioning their use of on-call shifts. The letters, which were first reported by The Wall Street Journal, said retailers were providing workers with “too little time to make arrangements for family needs, let alone to find an alternative source of income to compensate for the lost pay.”

Several companies that received letters from the New York attorney general have denied that they use on-call scheduling for low-wage workers, or that it is common in their stores. Some retailers say that only a small fraction of their workers who have been on unpredictable schedules care for children.

“Very few of our store associates are working parents,” said Michael Scheiner, a spokesman for Abercrombie & Fitch, which was among the letter’s recipients.

But the problem appears to be widespread. A 2012 study of nonfood retail workers in New York City by Stephanie Luce of the City University of New York and by the Retail Action Project, a workers’ advocacy group, found that more than half of the surveyed workers who cared for others, like children or elderly family members, had to make themselves available for last-minute shifts.

Because the practice is relatively new, however, scholars must infer its likely impact from research over the last decade showing the effects on children of parents working nonstandard hours, including night shifts, that have been more common for years.

In one of the most respected studies, published in 2005 in the journal Child Development, Prof. Wen-Jui Han of New York University looked at children during their first three years of life, controlling for such demographic variables as their mothers’ income, education, and race and ethnicity.

Professor Han, who was then at Columbia University, found that children of mothers who worked nonstandard schedules performed lower on problem-solving, verbal comprehension and spoken language tests than children of mothers who worked traditional schedules. Part of the explanation, she concluded, was increased stress on the part of the parents.

“Parents try their best to attend to their children in a sensitive and warm manner, but the physical and emotional exhaustion from nonstandard schedules makes it difficult,” Professor Han said in an interview. “With young children, if they’re crying, asking for food, asking for something, it’s all about how you interact with them.”

Another key issue, she found, was access to quality child care. Children whose mothers worked nonstandard schedules during their first year of life were significantly less likely to be enrolled in professional day care centers throughout early childhood. This type of child care setting, she noted in the paper, tends to be associated with better cognitive development than informal arrangements like relying on extended family members, a frequent alternative.

As for adolescents, Professor Han and two colleagues published a second paper, in the journal Developmental Psychology in 2010, which said that the longer mothers worked odd hours, the more likely their children were to smoke, drink, act out and engage in sexual activity.

The specific effect of on-call work and other frequently changing schedules — as opposed to work hours that fall outside the traditional workday — is only beginning to be studied, but social scientists worry that it has similar implications for children.

In a study of female workers at a large clothing retailer published last year in the Industrial & Labor Relations Review, Julia R. Henly and Susan J. Lambert of the University of Chicago found that the unpredictability of the workers’ schedules was related to higher stress and difficulties juggling work and family demands.

While the study did not examine the way this affected children, Dr. Henly suggested that the challenges posed by unpredictable work hours could take a toll on children as well. She also predicted that mothers with constantly changing work schedules would be less likely to enroll their children in preschool and other high-quality child care facilities.

“Some amount of early childhood education is important,” she said. “But it’s impossible to take advantage of those opportunities if you have a schedule that doesn’t allow you to get your kid there.”

According to Carrie Gleason of the Center for Popular Democracy, a nonprofit organization that helps community groups organize, such complications may explain why there appear to be fewer parents who work on-call shifts.

“A lot of times we find that they don’t last very long,” she said. “It’s absolutely impossible for working parents to meet their responsibilities to their families and hold down a job at a company with on-call shifts.”

Still, even parents who don’t work on-call jobs often have little advance notice of their schedules. In many companies that officially promise to make schedules available in advance, Ms. Gleason said, “managers edit the schedule up until the hours someone is supposed to come in.”