The rapid-fire push by the Trump administration to wipe out significant chunks of the Obama environmental legacy is running into a not-so-minor complication: Judges keep ruling that the Trump team is violating federal law.

The latest such ruling came late Wednesday, when a federal magistrate judge in Northern California vacated a move by the Department of Interior to delay compliance with rules curbing so-called flaring, a technique oil and gas companies use to burn off leaking methane. Flaring is blamed for contributing to climate change as well as lost tax revenues because the drilling is being done on federal land.

It was the third time since July that the Environmental Protection Agency or the Interior Department has been found to have acted illegally in their rush to roll back environmental rules. And in three other environmental cases, the Trump administration reversed course on its own after lawsuits accusing it of illegal actions were filed by environmental groups and Democratic state attorneys general.

The legal reversals reflect how aggressively Mr. Trump’s critics are challenging the administration’s efforts to rescind regulations enacted during the Obama administration, not only related to the environment, but to immigration, to consumer protection and to other areas.

Yet even as the list of failed or at least stalled rollbacks continues to grow, the Trump administration, in many other cases, continues to move ahead with its agenda, often trying a number of different approaches to killing the same rule, so that early setbacks do not necessarily mean anything has been settled.

“The Trump administration is confident in its legal positions and looks forward to arguing — and winning — before the federal judiciary,” Kelly Love, a White House spokeswoman, said in a statement. “This is in stark contrast to the previous administration, which may be the worst win rate before the Supreme Court since the Taylor administration in the early 1850s.”

Still, the string of court rulings and administrative reversals — even some conservative legal scholars agree — is a sign that the Trump administration has been in such a rush to undo the Obama legacy that it is almost inviting legal challenges.

“If I were in this administration, this should be seen as a warning sign,” said Jonathan H. Adler, the director of the Center for Business Law & Regulation at Case Western Reserve University School of Law. “The message is clear: Guys, we have a problem here. We are trying to do stuff that is hard and we are not crossing our i’s and t’s.”

Environmentalists see it as proof that Mr. Trump and his team care little about honoring federal law.

“It shows serial lawbreaking and sloppiness by a Trump administration bent on rollbacks,” said John Walke, the director of the clean air project at the Natural Resources Defense Council. “It is sad they have to have their comeuppance in courts rather than doing what was right.”

But this is hardly the first administration to have administrative decisions overturned as a result of court challenges. Environmentalists challenging the moves by George W. Bush to loosen air pollution rules won 27 court rulings during his eight-year tenure.

And the Obama administration itself was repeatedly challenged by environmentalists. In a recent decision related to two billion tons in coal leases on federal land in the Powder River Basin of Wyoming, for example, the United States Court of Appeals for the 10th Circuit concluded that the Democratic administration’s decision to approve the leases was “arbitrary or capricious” because it did not adequately consider the effect mining all this coal would have on climate change.

But even within the White House, there is awareness that the agencies need to be more careful to avoid further stumbles.

“There are concerns,” Neomi Rao, the head of the Office of Management and Budget division that oversees major federal rules, said in an interview this summer, shortly after she assumed her post. “Agencies want to move quickly to get things done.”

Policy experts say the reversals also underscore the fact that crucial positions within the E.P.A. and the Interior Department remain unfilled, and that a lack of trust exists between political appointees and career staff members.

“The career people at E.P.A. and D.O.J. are top-notch lawyers,” said Richard J. Lazarus, an environmental law professor at Harvard University. “But you have political people come in, and they don’t trust them at all and try to do it without them.”

Xavier Becerra, the attorney general of California, who has been perhaps the most aggressive of the state officials suing to challenge Trump administration rollbacks, said he hopes the White House is getting the message.

“No man, no woman is above the law,” Mr. Becerra said in an interview, shortly after the California magistrate judge ruled that the Interior Department had illegally postponed the enforcement of the methane flaring rule. “You have to follow the rule of law. It makes no difference if you are in the White House or not.”

Each of the rules at the center of these legal challenges has major public implications.

The Department of Interior methane rule reinstated by a federal court on Wednesday will annually eliminate the equivalent of greenhouse gas emissions from about 950,000 vehicles, according to an Obama administration estimate, while also generating millions of dollars in extra federal revenues because oil and gas companies right now do not pay royalties on methane they flare off in giant torches that light the sky.

But the Interior Department, under new leadership, argued that these environmental benefits were not worth the costs.

“Small independent oil and gas producers in states like North Dakota, Colorado and New Mexico, which account for a substantial portion of our nation’s energy wealth, could be hit the hardest,” Katharine MacGregor, a senior Interior Department official, said in a statement this spring.

The federal court judges were not impressed by the legal arguments the Interior Department and E.P.A. made as they separately moved to repeal the Obama-era rules related to methane, which is considered a major factor in climate change.

Efforts by Scott Pruitt, the E.P.A. administrator, to postpone his agency’s methane rule were “unlawful,” “arbitrary” and “capricious,” a three-judge panel said in July.

“Agencies obviously have broad discretion to reconsider a regulation at any time,” the judges ruled. “To do so, however, they must comply with the Administrative Procedure Act (APA), including its requirements for notice and comment.”

There are signs that the Trump administration is hearing this message. As in three other recent cases, the administration has given up efforts to roll back rules after lawsuits were filed to challenge them even before any judges had ruled on the merits of the arguments.

Those reversals involve rules intended to reduce asthma-causing ozone pollution, toxic mercury contamination in water supplies and a requirement that state transportation departments monitor greenhouse gas emission levels on national highways and set targets for reducing them.

Kyle Danish, who represents oil and gas companies and electric utilities for the law firm Van Ness Feldman in Washington, said the administration is learning an important lesson: even rolling back regulations involves bureaucracy.

“There’s an irony here that an administration that is upset about the administrative state is going to need multiple rules just to change the rules. But that’s the reality,” he said.

Not everyone is concerned by the court setbacks. Matt Letourneau, a spokesman for the U.S. Chamber of Commerce, called them “relatively minor blips in a much larger, longer-term effort,” and he noted that the Department of Energy has won recent cases against environmental groups related to the transport of liquefied natural gas.

Even with these setbacks, the list of environmental rules that have been delayed or reversed is considerable, including reversing freezes on new federal coal leases, offshore drilling in the Atlantic and Arctic Oceans and lifting mining restrictions in Bristol Bay, Alaska.

And just because courts are ruling against the Trump administration, it does not mean the fights are over.

On Thursday, for example, the day after the court overturned its effort to delay the flaring rule, the Interior Department posted a new notice in the Federal Register indicating its intent to delay the date again, until January 2019. This time, though, the agency is inviting public comments on the delay.

But there is no doubt the legal challenges are slowing down the march to roll back the Obama legacy. And it could complicate other even higher profile pushes to repeal rules, like the Clean Power Plan — intended to reduce carbon dioxide emissions from electric power plants, a move that will generate another wave of legal challenges that will build off arguments made in recent cases.

Mr. Lazarus said some problems might be alleviated once Mr. Trump nominates and the Senate confirms more high-level appointees, who have more experience in handing complicated legal steps needed to rollback rules.

But filling these jobs has been slow.

“There are a lot of fabulous Republican lawyers out there,” he said, “and a lot of them don’t want to be tainted by this administration.”