Federal agents and sheriff’s deputies streamed into the quiet desert subdivision by night. They stepped past spiky agave plants and surrounded a house, preparing to serve a search warrant. A couple of miles away, investigators descended on a parked Range Rover and draped it with evidence tape.
For the second time in the excruciating weeks since Nancy Guthrie vanished, Friday’s burst of law enforcement activity in a southern Arizona neighborhood signaled a possible break in a case that has transfixed the country.
But, once again, the authorities later announced a disappointing result: Even after one person was questioned and the S.U.V. was towed away, no arrests had been made and there had been no trace of the 84-year-old Ms. Guthrie.
By Monday, there were few visible signs of significant progress in an investigation that for more than 16 days has frustrated the police and tormented Ms. Guthrie’s family — most visibly, her daughter, “Today” show host Savannah Guthrie, whose public pleas for help have reached millions around the world.
As the search slogged into its third week, television trucks continued to line the street outside Ms. Guthrie’s home in Tucson, Ariz., which has also become a magnet for mourners and true-crime live-streamers. Amateur sleuths have dissected the shreds of public evidence and Pima County Sheriff Chris Nanos has tried to dispel rumors and far-fetched theories.
His department has received tens of thousands of tips, combed the neighborhood by foot and by air and enlisted the help of the F.B.I. and other agencies. Still, the authorities have not identified a suspect and they do not know whether Ms. Guthrie is still alive.
The uncertainty has investigators scrambling. Until they find Ms. Guthrie, they must assume she is in imminent danger, which means they are moving faster than normal, said Lance Leising, a retired F.B.I. agent in Phoenix.
“When you do that, you run the risk of hitting dry holes, of swinging and missing,” said Mr. Leising, who also stressed that the public is aware of probably only “5 percent of what investigators know.”
The anticlimactic operation on Friday night echoed a chapter in the investigation that unfolded a few days earlier, when officers descended on Rio Rico, Ariz., about an hour’s drive south of Tucson. They detained one man and held him for hours while they questioned him. Sheriff Nanos thought his team had cracked the case.
But before long, investigators acknowledged they had hit a dead end. They released the man and continued their increasingly desperate search.
Ms. Guthrie was taken in the early hours of Feb. 1, the police have said. She had plans to watch a church service with friends later that morning, and when she did not show, they called her oldest daughter, Annie, who rushed to Ms. Guthrie’s home and found it empty. Blood, which tests would later confirm belonged to Ms. Guthrie, was splattered across the front stoop.
The authorities have released little information about what else they found at the house in the foothills north of Tucson, but Sheriff Nanos said it looked like a crime scene.
The details that have emerged have been ominous.
One day after Ms. Guthrie vanished, a Tucson-area television station received a ransom note purporting to be from her kidnapper. TMZ, the celebrity gossip outlet, received a similar note the next morning and reported that it demanded millions of dollars in Bitcoin for Ms. Guthrie’s return.
The F.B.I. advised the Guthrie family on how to proceed, and Ms. Guthrie’s three children released a statement telling the supposed kidnapper they were “ready to talk.” But the authorities have acknowledged the note may have been sent by an impostor. TMZ reported on Monday that it had received four such communications in all.
Perhaps the most tangible lead materialized on Feb. 10, when federal officials released photos and video recovered from Ms. Guthrie’s doorbell surveillance camera. The haunting images show a masked man approaching the door wearing gloves and a backpack, with what appears to be a handgun holstered at his waist.
The pictures opened up several new investigative avenues. Police officers sought to track down the source of the man’s clothing, which they said may have been purchased at Walmart. Then, on Feb. 12, sheriff’s deputies searching a field two miles from Ms. Guthrie’s home discovered discarded gloves that appeared to match the pair worn by the man in the surveillance video.
Preliminary testing revealed the gloves carried the DNA of an unknown man, and F.B.I. analysts were planning to enter the sample into a database. The process can take about 24 hours, officials said.
As they worked, the area around Ms. Guthrie’s house, once the site of steady activity, grew quiet. Online, armchair investigators puzzled over clues and speculated wildly. And Ms. Guthrie’s family projected hope.
“We still believe,” Savannah Guthrie said in a video posted to social media on Sunday evening
She did not mention a ransom, nor did she reference other details from the case.
Instead, she appealed directly to her mother’s captor: “It is never too late,” she said, “to do the right thing.”
Reis Thebault is a Phoenix-based reporter for The Times, covering the American Southwest.
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