Three years after that secret arrival, the Taliban officials remain idle and their political office here remains unused.

“They are just living here enjoying the air-conditioning, driving luxury cars, eating and making babies,” one Afghan diplomat in Qatar said. “It’s all they can do; they have no work to do.”

They are unlikely to see a negotiating table anytime soon either, with the new fighting season in Afghanistan off to a particularly violent start and with the latest push to restart talks all but abandoned. Once again, the Taliban’s attention is on the battlefield, and on what may be gained or lost there as the American military begins its withdrawal from the war.

The Taliban presence here — eight or more relatively high-ranking officials with their families, Afghan officials say — is occasionally reconfirmed in a sighting on the streets or, in the case of the Afghan diplomat, when the Taliban men come to the sleepy Afghan Embassy here to register the birth of another child.

Early insurgent negotiations with American officials had a faltering start, initially over a proposed prisoner exchange, in which five Taliban figures being held at Guantánamo Bay, Cuba, would be released in exchange for the freedom of the lone American soldier being held prisoner by the Taliban, Sgt. Bowe Bergdahl. But American officials say that their talks have ended and that there have been no further discussions with the Taliban since early 2012.

Recently, Western diplomats in Kabul, Afghanistan’s capital, expressed hope that the discussions might resume amid intense diplomatic activity by many countries to push peace talks, this time led by Afghanistan. That hope now appears to have fizzled once again, and diplomats’ expectations of some movement by the end of March from the Taliban side have come to naught. President Hamid Karzai met here with the Qatari emir,Sheik Hamad bin Khalifa al-Thani, on March 31 in what Afghan officials billed as discussions about opening the office, but no developments were announced after the meeting.

“There is a limit to how long we can wait,” said another Western diplomat familiar with the peace efforts. “If at some point they don’t issue statements, it’s not open-ended. There are ways we can pressure the Taliban in Qatar.”

Officially, the Qataris have never explicitly admitted that the Taliban are even present here, and the government-controlled press never mentions it, although they have acknowledged that they are willing to host an official office for peace talks.

Qatari officials did not respond to requests for comment about the Taliban presence.

“With the Taliban, the Qataris have a hot potato,” said an Afghan journalist working here, who spoke on the condition of anonymity for fear of being expelled. “How do you handle hosting suicide bombers? They can’t acknowledge them until that sort of activity stops.”

The Taliban representatives here are not lightweights. The most prominent among them isTayeb Agha, the chief of staff to the Taliban’s leader, Mullah Muhammad Omar. Others include Sher Mohammad Abbas Stanikzai, the former Taliban health minister, and Qari din Mohammed Hanafi, their former minister of planning. The delegation includes veteran diplomats like Mualavi Shahabadin Delawar, the former Taliban ambassador to Saudi Arabia; Sohail Shaheen, a former ambassador to Pakistan; and Hafiz Aziz Rahman, the representative to the United Nations for the Taliban government when it ruled Afghanistan.

Just why the effort to open a Taliban office has faltered is a matter of dispute. The Americans say the Taliban have simply decided to continue fighting, worried by pressure from their own hard-liners and concerned that entering peace talks would sap their will on the battlefield. “No one wants to be the last one to die before peace talks start,” as one diplomat put it.

The Taliban say the Americans reneged on their confidence-building pledge to free the Guantánamo five, which would have been politically difficult for President Obama, given bipartisan opposition in Congress to such releases. Instead, the Americans insisted that talks would have to include the Afghan government first. The Taliban has rejected that condition, deriding the government of President Hamid Karzai as a puppet regime and saying it would talk to the Afghan government only after reaching a settlement with the Americans.

Still, neither Western diplomats nor the Taliban have given up on the idea of talks in Qatar. “There are Taliban all over the place talking about peace, but the U.S. government’s view is that the most promising is the Doha track,” one diplomat said.

Wahid Muzhda, a former official in the Taliban’s Foreign Ministry who now lives in Kabul but maintains contacts with the insurgents, said that “some of the Taliban still believe it’s worth having the office there, but its prospects do look dim.”

Both Taliban and American officials publicly agree on one thing: that they are no longer talking to each another, officially or unofficially.

That, however, is a development that the Afghan government has refused to believe. President Karzai has openly accused the Americans of doing so. “We think they are secretly talking,” the Afghan diplomat in Qatar said. “America is the best friend of Afghanistan, and between friends we should tell each other what we’re doing.”

The Afghans have not tried to block the Qatari initiative. “It suits everybody,” said the Afghan journalist working in Doha. “The Americans want their soldier back, the Taliban want a vacation, the Pakistanis want the Taliban to look independent of them, and the Afghans want distance between the Pakistanis and the Taliban.”

While in Qatar, the Taliban have scrupulously avoided all public appearances, refusing interviews and issuing no statements — which the Qataris have made a condition of their presence.

An Afghan diplomat was at a shopping mall in Doha recently and heard a child call out in Pashto, the language used by most Taliban.

The diplomat turned and saw Hanif din Mohammad, a Taliban representative from northern Badakhshan Province. Introducing himself as an embassy official, the diplomat then said, “So, are you from the other side?” Blushing, the Talib turned and walked away, children in tow.