The day after New Year’s, John Reichert of Boulder, Colo., had a heated argument with his 14-year-old son, James. “I’ve failed you as a father,” he told the boy despairingly.

During the long months of lockdowns and shuttered schools, Mr. Reichert, like many parents, overlooked the vastly increasing time that his son was spending on video games and social media. Now, James, who used to focus his free time on mountain biking and playing basketball, devotes nearly all of his leisure hours — about 40 a week — to Xbox and his phone. During their argument, he pleaded with his father not to restrict access, calling his phone his “whole life.”

“That was the tipping point. His whole life?” said Mr. Reichert, a technical administrator in the local sheriff’s office. “I’m not losing my son to this.”

Nearly a year into the coronavirus pandemic, parents across the country — and the world — are watching their children slide down an increasingly slippery path into an all-consuming digital life. When the outbreak hit, many parents relaxed restrictions on screens as a stopgap way to keep frustrated, restless children entertained and engaged. But, often, remaining limits have vaporized as computers, tablets and phones became the centerpiece of school and social life, and weeks of stay-at-home rules bled into nearly a year.