LONDON — Queen Elizabeth II will mark 70 years on the throne in February, a milestone unmatched by any British sovereign and a chance to turn the page on three years of ceaseless turmoil in the royal family. But a sexual-abuse lawsuit unfolding in a Manhattan courtroom could yet spoil her celebration.

On Tuesday, lawyers for the queen’s second son, Prince Andrew, asked a federal judge to throw out a lawsuit by Virginia Roberts Giuffre, in which she claims that Andrew, a friend of the late financier and convicted sex offender Jeffrey Epstein, raped her when she was 17.

It was the latest in a skein of legal maneuvers by the prince’s lawyers to defuse Ms. Giuffre’s case. While the judge, Lewis A. Kaplan, did not immediately rule on the motion, leaving Andrew’s legal fate unsettled for now, the hearing dramatized the shadow that the 61-year-old prince still casts over his family.

If the judge allows the case to go forward, Andrew could face damaging testimony from Ms. Giuffre about his alleged abuse of her at Mr. Epstein’s residences in New York and in the Caribbean. That would plunge the House of Windsor back into scandal at the very moment it hopes to use the Platinum Jubilee to remind Britons of the queen’s extraordinary longevity and largely blemish-free record of service.

The 70-minute hearing gave a glimpse into the kinds of issues that could spill out in a prolonged trial. At one point, Prince Andrew’s lead lawyer, Andrew B. Brettler, argued that Ms. Giuffre had not been specific in her allegations against him. Judge Kaplan replied that she claimed she had been subjected to “involuntary sexual intercourse” and asked what was not clear about that.

“If the case drags on and on and on, yes, it will be a thorn in the side of the Platinum Jubilee,” said Dickie Arbiter, who served as a press secretary to the queen from 1988 to 2000. Beyond the fraught issues raised in that case, he said, were the lingering questions stirred by the rift between the family and Prince Harry and his American-born wife, Meghan.

Harry, the queen’s grandson, plans to publish a memoir late in 2022, which has unsettled people around the royal family who fear further unflattering details about what the estranged prince and Meghan have claimed was callous and racist treatment at the hands of members of the royal family.

Andrew’s woes, by contrast, are largely of his own making, royal watchers point out, the product of his association with the disgraced Mr. Epstein and another friend, Ghislaine Maxwell, who was convicted last week of conspiring with Mr. Epstein to recruit, groom and abuse underage girls. Ms. Giuffre contends that she was among those victims; Andrew denies her claim that she was trafficked to him.

The queen has already largely banished Andrew from public life, a process that gained momentum after a calamitous interview he gave the BBC in November 2019, in which he tried to explain his friendship with Mr. Epstein and denied the allegations of sexual misconduct, saying he had no memory of meeting Ms. Giuffre. He no longer appears at public events, or even military ceremonies, and the British media’s coverage of him is uniformly scathing.

When photographers capture Andrew’s image — often at the wheel of a car coming or going to visit his mother — he appears a graying, weary shadow of the once-dashing helicopter pilot who beguiled the country with his service in the Falklands War and his busy bachelorhood.

“My gut feeling is that most people have lost interest in him,” said Penny Junor, a royal historian. “He’s arrogant and not particularly popular. Since he’s gone past middle age, there’s been a general sense of ‘what’s he for?’”

In one respect, however, Andrew could remain a lingering problem, Ms. Junor said. The queen has not stripped him of his honorary military titles, some of which he inherited from his father, Prince Philip, who died last year. That has prompted objections from veterans, who say it is unseemly to be under the command of a person facing such allegations.

Julian Perreira, a former sergeant in the Grenadier Guards who served in Afghanistan, told The Times of London last week, “Being allowed to retain his role as colonel of the Grenadier Guards and other military titles, Prince Andrew will put a stain on the regiment’s proud history and will devalue the hard work of past and future generations of Grenadiers. He must step down immediately.”

Prince Harry was stripped of his honorary military titles — as well as the right to use the honorific His Royal Highness — after he and Meghan stepped back from official duties and moved to Southern California.

For Andrew to retain his titles, even while being accused of sexual misconduct, strikes some in Britain as the ultimate illustration of a double standard for privileged members of the royal family. It would be all but impossible to defend if he is found guilty of abusing an underage girl.

Andrew’s reputation, critics say, has not been helped by his legal maneuvering. Rather than confronting the allegations directly, the prince scrambled to avoid being served with legal papers in Britain. His lawyers have tried to get the case dismissed on jurisdictional grounds and, most recently, on the basis of a settlement agreement between Ms. Giuffre and Mr. Epstein.

Under the terms of that 2009 agreement, unsealed on Monday, Mr. Epstein paid Ms. Giuffre $500,000 to resolve a lawsuit in which she accused him of sexually abusing her when she was a teenager. Ms. Giuffre, in turn, agreed to release Mr. Epstein and other “potential defendants” from further litigation, a category that Andrew’s lawyers said included him.

But Ms. Giuffre’s lawyer, David Boies, argued in court that Andrew was not a target of the allegations of sexual trafficking made by Ms. Giuffre in 2009. Hence, he is not protected under the terms of the settlement. “He was someone to whom the girls were trafficked,” Mr. Boies told the judge. “He’s not a potential defendant.”

While Judge Kaplan did not indicate how he was leaning in whether to dismiss the case, he pointedly allowed the process of gathering evidence to continue. That will keep the legal pressure on Andrew. And it will make for a tense start to the Platinum Jubilee year for the queen, who has already been struggling with health problems that have kept her out of public view since October.

The queen, royal watchers note, has been steadfast in her affection for Andrew, even as his public reputation has withered. Having gone along with sidelining her son — a step that was pushed by her eldest son and heir, Prince Charles — some doubt that she would strip Andrew of his titles.

“The queen gives and the queen takes away, but she’d probably be reluctant to take this away because that’s all he got left,” Mr. Arbiter said. “She is the head of state and head of the nation, but at the end of the day, she’s also his mother.”