An Alabama death-row inmate who missed an appeal deadline because of a mailroom mix-up at a New York law firm received an especially sympathetic hearing from the Supreme Court on Tuesday.

Across the court’s ideological spectrum, the justices seemed to be searching for a way to grant Cory R. Maples — who is not claiming innocence in a double murder — a chance to pursue in lower courts his claim of ineffective counsel at his trial and sentencing.

He missed the deadline for making those claims after the notice of a judge’s ruling in the case was returned unopened from the mailroom of the firm of Sullivan and Cromwell. Two junior associates who had agreed to represent Maples in his post-conviction appeals left the case without telling him. A county clerk did nothing more when he received the letters marked “return to sender.”

Justice Samuel A. Alito Jr., a former federal prosecutor who usually is in the government’s corner in criminal cases, told Alabama officials that he could not understand why they would contest Maples’s request for a new hearing.

“Mr. Maples has lost his right to appeal through no fault of his own, through a series of very unusual and unfortunate circumstances,” Alito told Alabama Solicitor General John C. Neiman Jr. “Now, when his attorneys moved to file an out-of-time appeal, why wouldn’t you just consent to that?”

Neiman disputed that Maples had been abandoned by his attorneys. He said the inmate was represented at all times by local counsel and that other attorneys at Sullivan and Cromwell were preparing to help him. But Neiman did not find much support on the bench.

“We know that the two who were listed as counsel of record were not representing him and they hadn’t told the court,” Justice Ruth Bader Ginsburg said flatly.

And Chief Justice John G. Roberts Jr. discounted the role of the local attorney, who Maples said was involved in the case only because Alabama required at the time that a local lawyer be part of the proceedings.

“You still haven’t told me one thing he did more than move the admission of the out-of-town attorneys,” Roberts told Neiman sternly after an extended round of questioning.

Neiman’s only vocal support came from Justice Antonin Scalia.

“Once you are in court and you have a lawyer, it’s up to your lawyer to follow what goes on in the court,” Scalia said. “That’s the assumption of the federal rules. And it seems to me a perfectly reasonable assumption. And I’m not about to hold that they are unconstitutional simply because an extraordinary requirement of notice . . . has gone awry.”

Gregory G. Garre, who was a solicitor general in the George W. Bush administration and was recruited by Sullivan and Cromwell to represent Maples at the high court, told the justices that the case was “sui generis,”Latin for unique. “The facts are extraordinary, the facts are shocking,” he said.

Maples was convicted of shooting two acquaintances in the head in 1995. He stole money and a car, and he confessed when captured two weeks later.

He was represented at trial by two young lawyers who were paid $1,000 for their work, and a jury recommended death by a vote of 10 to 2, the minimum necessary under Alabama rules.

Maples said he thought he had “hit the lottery” when the New York lawyers offered to help him. They filed a motion on his behalf alleging ineffective counsel. But in the 18 months it took for the Alabama judge to render his negative ruling, each had moved on to other jobs.

On Tuesday, the justices and the lawyers took turns suggesting who might be responsible for mishandling Maples’s case. Justice Elena Kagan was critical of the Alabama court clerk who did nothing when two of the three letters he sent concerning the order were returned unopened. Roberts said it was critical to discern how involved the local lawyer was in Maples’s defense.

Others mentioned more senior lawyers at Sullivan and Cromwell who may have been supervising the young lawyers.

But the justices seemed most concerned about finding a narrow way to resolve Maples’s case without broad new rules that would encourage even more death-row appeals.

The court has previously held that the mistake of an attorney in post-conviction proceedings must be borne by his client. But Garre said the difference in this case was that the lawyers abandoned Maples.

He suggested that the court could use that difference to instruct the lower court to look again at Maples’s appeal.

The case is Maples v. Thomas.