“Sometimes the magic works, sometimes it doesn’t,” said Daniel R. Russel, an assistant secretary of state under President Barack Obama.
While Mr. Warmbier was put on trial and his family knew he was being held by the North Korean government, Mr. Tice’s case has been a conundrum. The United States believes the Syrian government is holding him, but it has no proof. Syria insists it does not know what happened to him.
“Austin Tice is not in the hands of Syrian authorities, and we don’t have any information about him at all,” Deputy Foreign Minister Faisal Mekdad told The Associated Press last year.
The Tice family declined to comment, as did the C.I.A. and the F.B.I.
Mr. Tice, a former Marine captain from Texas, left for Syria before his final year in Georgetown Law School. He traveled to the region and had been freelancing for news media outlets when he was abducted in August 2012.
A month later, Mr. Tice appeared blindfolded in a video that shows masked men with assault rifles. Looking scared and disheveled, he uttered a few words in Arabic and then vanished. Former American officials believe that the government of President Bashar al-Assad of Syria took Mr. Tice and that the video was a crude ploy to blame militants for his abduction.
Despite its antagonistic relationship with the United States, there is ample motive and precedent for the Syrian government to speak with high-level American officials. Before the civil war, there were several such contacts, including one in 2010 between Mr. Mamlouk and Daniel Benjamin, who served as the coordinator for counterterrorism in the State Department in the Obama administration.
Even after the war broke out and the United States adopted a policy of pushing for Mr. Assad’s ouster, Syrian officials were open to communicating with Americans, diplomats say.
“The Syrian government would like to reduce the extent of its isolation,” said Robert S. Ford, an American ambassador to Damascus during the Obama administration. “The Syrians are a very supple, nasty group. They’re willing to talk all the time. That’s just how they do business.”
After the election, American officials decided to brief Jared Kushner, President Trump’s son-in-law, and the president’s chief strategist, Stephen K. Bannon, about the efforts to bring Mr. Tice home. Mr. Bannon was dismissive of Mr. Tice, raising questions about why he had traveled to Syria in the first place, former officials said.
Still, after Mr. Trump took office, the administration moved forward, resulting in Mr. Pompeo’s phone call with Mr. Mamlouk in which he raised the issue of Mr. Tice. It is not clear what exactly the two men said, but the United States later suggested to Mr. Mamlouk that freeing Mr. Tice would go a long way as the administration shaped its broader Syria policy, according to the former officials.
It seemed like the best chance yet to bring Mr. Tice home. Administration officials began trying to figure out how the Syrians might explain his lengthy disappearance. After the Americans received proof of life, the Syrians would announce they had found Mr. Tice, crafting a narrative to explain his abduction. Mr. Tice would be put on trial for violating the country’s immigration laws and then pardoned by Mr. Assad. After Mr. Tice landed on American soil, Mr. Trump would call Mr. Assad.
But that never happened, and some former diplomats pointed to a comment in March by Nikki R. Haley, the American ambassador to the United Nations, who said the United States did not view Mr. Assad’s removal as a policy priority. “You pick and choose your battles,” Ms. Haley told reporters, “and when we’re looking at this, it’s about changing up priorities. And our priority is no longer to sit there and focus on getting Assad out.”
Her comments were unusual, former diplomats said. The administration had weakened its negotiating position by giving the Syrian government something it wanted — the president’s tacit approval of Mr. Assad — without demanding anything in return.
“The administration said Assad could stay but got nothing for it,” said James O’Brien, the former special presidential envoy for hostage affairs under the Obama administration. “You only make that statement if you get Austin Tice home.”
Andrew J. Tabler, a senior fellow at the Washington Institute for Near East Policy, said that it was always going to be hard to get Mr. Tice out of Syria but that recent events had made it even harder. “What the regime requires is for us to overlook what they do,” Mr. Tabler said, referring to the gas attack. “That’s a big deal. There is no way the U.S. is going to ignore these actions.”
American officials suspect that Mr. Mamlouk or Brig. Gen. Bassam al-Hassan, an adviser to Mr. Assad, knows Mr. Tice’s whereabouts. Like Mr. Mamlouk, Mr. Hassan has been hit with sanctions by the United States.
Last year, the American intelligence community concluded with moderate to high confidence in a secret analysis that Mr. Tice was alive, based partly on a report that he had been seen at a hospital in Damascus, being treated for dehydration.
Mr. Tice was not the only American held in Syria. Kevin Patrick Dawes, a freelance photographer from San Diego, was abducted in 2012 by government forces. In late 2014, the Syrians acknowledged holding Mr. Dawes, then freed him in April 2016 for health reasons, officials said.
At times, the Russian government, which is allied with Syria, tried to parlay the release of Mr. Tice, Mr. Dawes and others with ties to the United States who were being held in Syria to its advantage. In talks with American officials, the Russians suggested they might be able to help in exchange for the release of Russians imprisoned in the United States. The Americans also floated the idea of freeing a Russian spy for Mr. Tice, but Russian officials did not respond to the offer.
Ultimately, American officials concluded that the Russians did not know where Mr. Tice was or who was holding him.
Several Americans also remain held in Iran, including an elderly father and his son, and a former F.B.I. agent and C.I.A. contractor, Robert A. Levinson, who disappeared on the island of Kish in 2007. At least three others are still being detained in North Korea. Officials worry the government there could arrest more.
The momentum to free Mr. Tice came to a halt in April when the Syrian government unleashed the gas attack on its own civilians, killing dozens of men, woman and children. In the days that followed, Mr. Trump ordered a strike on a Syrian air base used to carry out the gas attack.
Mr. Trump said in a recent interview that Mr. Assad was “truly an evil person.” The situation only worsened in recent days as the United States shot down a Syrian fighter jet.
Mr. Tabler said the time was not right for a deal over Mr. Tice, who will turn 36 in August. “We’re not there,” he said. “That’s sad for Austin Tice and his family. Everybody wishes that it had been different. That’s just a hard reality.”