Lawyers for Donald J. Trump have spent this week seeking to stave off the former president’s trial on charges that he covered up a sex scandal.

They tried again Wednesday. Again, they failed.

In Mr. Trump’s latest last-minute bid to delay a trial that starts Monday, he filed a civil action in an appeals court against the judge in the case, Juan M. Merchan. It sought to delay the trial while the appeals court reconsidered several of the judge’s rulings.

A single appellate court judge, Ellen Gesmer, promptly rejected Mr. Trump’s request. Mr. Trump can now have his action heard by a full panel of five appellate court judges, but it would be nearly impossible for the court to act before the trial begins.

The episode underscored Mr. Trump’s increasing desperation to delay the trial, and his scattershot approach to doing so.

Stalling is one of the former president’s favorite legal strategies, in the Manhattan case and all his many legal entanglements. But even for Mr. Trump, it was an audacious move: taking legal action against a judge and burying an appeals court in long-shot delay tactics.

Nearly a dozen legal experts contacted for this article strained to recall any other defendant filing three emergency appeals in three days. Most called it unprecedented; one called it “silliness.” And at this rate, with five days to go before jury selection and a smattering of other legal issues still unresolved, Mr. Trump might not be done.

Barry Kamins, a former New York judge who is now a defense lawyer, said the three-time effort was unusual. But, he added, “​I’ll ask you: Has a former president ever been prosecuted before? Everything about this case is a first.”

The papers on Wednesday included a request that the appeals court pause the case while it considers whether to oust Justice Merchan. Mr. Trump’s lawyers argue that Justice Merchan has a conflict of interest, citing his daughter’s work as a Democratic political consultant.

Ethics experts have said that Justice Merchan does not need to step aside, and the judge has previously declined to recuse himself, noting that a judicial ethics panel concluded last year that he had no real conflict. The Trump team recently asked Justice Merchan again to step aside, and the judge is expected to give his answer this week.

“There is absolutely no evidence to show that Judge Merchan will stand to benefit from the outcome of this trial,” Lisa Evans, a lawyer for the court system, said at a hearing on Wednesday.

Mr. Trump’s action against the judge — a special proceeding known as an Article 78, which comes in the form of a lawsuit and is used to challenge New York State agencies and judges — was first reported by CNN.

In the action, Mr. Trump’s lawyers also asked the appeals court to prevent prosecutors from presenting certain evidence about their client related to his duties as president. Justice Merchan has rejected that argument, and a lawyer from the Manhattan district attorney’s office said Wednesday that the last-minute filing was not an appropriate way to make it.

That lawyer, Steven Wu, said that any delay would be “incredibly disruptive,” adding that there was a “powerful public interest” in ensuring that the trial went forward on Monday.

A lawyer for Mr. Trump, Emil Bove, agreed that the trial was of huge importance, but argued that public interest required the appeals court to intervene.

“This can only be done once, and it must be done right,” he said.

For Trump, there could be political advantages in losing the appeals. He could use the court’s denials as ammunition for his claims that the legal system was biased against him.

The Manhattan case that Mr. Trump is trying to avoid was brought by the district attorney, Alvin L. Bragg. It would be the first trial Mr. Trump faces after four indictments in four different cities.

Mr. Trump’s first effort this week to delay the Manhattan case was a more traditional appeal, a request to delay the trial while judges considered a defense request to move it outside Manhattan. It was denied Monday.

In a separate Article 78 action filed against Justice Merchan that day, Mr. Trump’s lawyers asked the appeals court to delay the trial while it considered his request to throw out a gag order the judge imposed. The order prohibits Mr. Trump from attacking witnesses, prosecutors and the judge’s family.

But Mr. Bragg has argued that the gag order will protect the people involved from Mr. Trump’s heated rhetoric. And an appeals court judge on Tuesday declined to pause the case.

Mr. Bragg accused Mr. Trump of falsifying records to conceal a sex scandal involving the porn star Stormy Daniels. The criminal case is one of four facing Mr. Trump, who is once again the presumptive Republican nominee for president, and it might be the only one of Mr. Trump’s criminal cases to make it to trial before Election Day this year.

If Mr. Trump wins the election, the cases will most likely grind to a halt.