Mr. Richardson, who has negotiated prisoner releases from Cuba to North Korea, had State Department approval to present at least two things, said four people with knowledge of the negotiations. One was a process for removing Cuba from the list of states sponsoring terrorism. The Obama administration was also willing to waive probation for one of the “Cuban Five,” as a group of Cuban agents accused of espionage in the United States are known on the island, so he could go home after he leaves prison next month.

But it was not enough. Mr. Richardson was not even allowed to see Mr. Gross, and when he left Havana on Wednesday, he was angry and disappointed, concluding that elements of the Cuban government “do not seem to really want warmer relations.”

That brand of bitterness is once again the modus operandi for United States-Cuba relations. American officials and experts say that Mr. Richardson’s failed trip was just the latest in a series of misunderstandings, missteps and perceived slights showing that both countries, after a moment of warmth, have slipped back into a 50-year-old pattern of cold distrust.

“Neither side has shown the slightest interest in learning from experience and have demonstrated repeatedly the tragic way in which both sides are condemned to repeat their mistakes,” said Robert A. Pastor, a professor at American University who advises former President Jimmy Carter on Latin America. “It’s not just the Obama people. It’s the new people under Raúl Castro.”

This is not what either side expected. President Obama campaigned for greater engagement with Cuba, boldly telling a Miami audience in May 2008 that he would be open to meeting with Mr. Castro and forging warmer relations. Four months after he took office, he headed in that direction, abandoning longstanding restrictions on the ability of Cuban-Americans to visit the island and send money to relatives.

The Cuban government responded quickly. Meetings with American officials became more common during the first year of the Obama administration, including a gathering in Havana with the highest-ranking State Department official to visit Cuba since 2002. Cuba also eliminated a 10 percent tax on remittances that had galled Cuban-Americans sending money to their families.

But the Gross affair cast doubt into the relationship. A contractor for a company financed by the United States Agency for International Development, Mr. Gross was arrested in December 2009. Cuba charged him with crimes against the state for delivering banned equipment as part of a semicovert program aimed at weakening the Cuban government.

The arrest sent a chill through the diplomatic corps of both countries. The Cuban government has complained for years about “democracy programs” it says subvert its authority and sovereignty. Still, American officials said they did not expect a protracted affair. Indeed, relations were still good enough a month later to lay the groundwork for what some officials now see as a lost opportunity — a jointly run medical clinic in Haiti.

The idea emerged soon after the earthquake that flattened Haiti’s capital, Port-au-Prince, in January 2010. Cuba quickly approved an American request to fly victims to Florida through Cuban airspace, and the country’s doctors won accolades from American officials.

That led to the idea for a more formal relationship and a new hospital for rural Haiti — in an area later ravaged by cholera. It was to be built and supplied with American aid, but staffed with Cuban doctors. According to current and former American officials, discussions moved smoothly over several months and were nearly complete when old sensitivities emerged.

“First the Cubans said, ‘We want to do this but you have to stop your efforts to recruit our medical brigades,’ ” said one American official who was not authorized to speak publicly. The Cubans were angered by a little-known program, started by President George W. Bush and continued by Mr. Obama, that assists Cuban doctors looking to defect, said several American officials.

Then, after the Obama administration signaled that it would not eliminate the program, Cuban officials were further incensed by an event at which they believed their country’s doctors were not given proper credit for their work in Haiti. Finally, just days before the agreement was to be signed, the Cuban government demanded that a second clinic be built in Port-au-Prince, at a cost of several million dollars. That killed the deal.

And from there, the relationship has continued to wither.

American officials say the Cubans missed an opportunity this year, when the White House and Senator John Kerry pushed to cut money for the democracy programs. If Cuba had released Mr. Gross then, officials said, the programs would have become less about weakening Cuba’s government and more about building civil society. Instead, Congress kept them largely intact.

For some time now, American officials said, Cuba has seemed uninterested in letting Mr. Gross go. The island of 11 million people is in the midst of its largest economic overhaul since the end of the Soviet Union — with a major drive toward private enterprise — and many Cuba experts believe that the country’s officials are engaged in an ideological war over how far and fast to go. Relations with the United States appear to have become secondary to domestic concerns, some argue. Or, they say, hard-liners seem to be winning the argument on foreign relations.

So while Mr. Richardson traveled with encouragement from the State Department, on what was officially labeled a private trip, several government officials said they were not surprised that his effort failed.

Mr. Richardson said that he had been invited, and that he had expected at least a meeting with Mr. Gross. Josefina Vidal Ferreiro, the Cuban Foreign Ministry’s head of North American affairs, said Mr. Richardson had gone to Cuba “on his own initiative.” She did not discuss the broader strain in relations. But signaling that removal from the terrorism list and a minor change in the sentence of an accused Cuban spy was not sufficient, she said the release of Mr. Gross “was never on the table.”

And it may not be anytime soon.

One thing that might move Cuba, said an official who has negotiated the issue, is if the European Union changes its common policy limiting relations with Cuba because of human rights concerns. But he and other American officials said that until Cuba released Mr. Gross, Cuba would continue to be isolated. For now, his release — along with many issues involving Cuba — appears to be caught in an echo chamber of grievance shaped by decades of failed attempts at warmer United States-Cuba relations.