Now, Cuba's Roman Catholic Church is fighting back.
Church officials on the island have launched a full-throated defense of their leader, and Catholic publications have harshly denounced his critics.
Analysts say the increasingly virulent back-and-forth is extremely unusual on an island where the church has traditionally preferred to exercise influence quietly, behind the scenes.
And it comes at a time when the cardinal could have reasonably expected to be taking a victory lap; he has just organized a high-profile visit by Pope Benedict XVI and is likely nearing the end of his tenure.
As is customary, Ortega handed his resignation to the pope when he turned 75 last year, but Benedict has not yet accepted it.
"What surprises me this time is not that there are attacks, because there have always been attacks," said Carlos Saladrigas, a Cuban-American businessman and one-time hardline anti-Castro militant who has become a voice for reconciliation between Miami and Havana.
"It's the voracity of the attacks, their forcefulness."
Ortega's troubles began shortly before Benedict's March 26-28 visit, and many believe they are a direct result of concessions the cardinal made to ensure its success.
Some say he held back criticism of the government in the months preceding the trip, and looked the other way as some dissidents were rounded up.
Then, days before Benedict arrived, Ortega had police called in to break up a sit-in at a Havana church by a group of protesters who were demanding a papal audience and political change on the island.
In a speech at Harvard University in April, Ortega defended the eviction and described the protesters as "former delinquents" with "no culture."
He also insisted that he had acted properly in helping negotiate the release of dozens of political prisoners in 2009 and 2010.
Most of the freed prisoners accepted exile in Spain, and some have since criticized Ortega for not doing enough to fight for their right to remain in their homeland.
Ortega told the audience at Harvard's Rockefeller Center of Latin American Studies that the prisoners' own families had requested exile, a version the family members deny.
The blowback to Ortega's speech was immediate, and sharper than any the cardinal has faced during a long career atop the island's Catholic hierarchy.
"Ortega's attitude only demonstrates his political complicity with the government," the director of U.S.-funded Radio and TV Marti Carlos Garcia-Perez wrote in an editorial in April. "This is a lackey's attitude."
Exile blogs in South Florida began calling for Ortega's resignation. One political cartoon that appeared in Miami's El Nuevo Herald showed the cardinal and a military-clad Castro singing a love song together.
Another depicted a snobby priest telling a worshipper that Ortega required proof of his cultural worthiness before he would be allowed to attend Mass.
In response, Church publications have put out a series of articles and editorials lauding Ortega as a brave advocate for Cuba's dissidents, and one of the few people on the island with the courage to speak his mind directly to Castro.
Supporters say Ortega has prodded Castro in face-to-face meetings to open the country to more private enterprise, and has allowed Catholic magazines to publish essays on the need for more reform that would never have been allowed in the state-run press.
In a letter emailed to foreign journalists on Monday, a council of Catholic community groups in Havana called Ortega a patriot who is motivated by love for Cuba and the church to bring about dialogue.
Cuban bishops issued an earlier statement saying they saw in the recent criticism a plan to destroy Ortega's reputation and harm the church.
By far the strongest defense has come from Orlando Marquez, a top church spokesman who published a battle cry against his boss's critics last month.
"Those who repudiate dialogue will never cease to open fire because that is their mission," Marquez wrote in Palabra Nueva, the Catholic magazine he puts out. "They want to blow up any effort at understanding."
Those sentiments — if not the belligerent phrasing — have been echoed by many of Ortega's allies, including Saladrigas and Miami Archbishop Thomas Wenski, who has long pushed his flock toward greater dialogue with their homeland.
"To suggest that somehow he is a lackey of the regime is ludicrous," Wenski told The Associated Press. "Some of the cardinal's harshest critics here are looking for a scenario that is easy to advocate outside of Cuba. They are thinking that there is some way to bring down the Cuban regime overnight."
Still, the cardinal's problems are not limited to Miami. Several prominent dissidents have been critical in recent weeks.
Guillermo Farinas, a hunger striker and winner of Europe's 2010 Sakharov prize, has called the cardinal a sellout.
Martha Beatriz Roque, a former political prisoner, accused him of bowing his head before the government.
Ortega met for more than three hours on June 7 with members of the island's best known opposition group, the Ladies in White, in an effort to clear the air. Ladies leader Bertha Soler said that she was satisfied with the meeting and that the cardinal "was very receptive."
But she made clear that she would keep pressure on the cardinal to advocate on her group's behalf, saying: "Our main objective here is for the Cardinal to know that we are women who get thrown in jail and suffer repression."
Enrique Lopez Oliva, a professor of religious history at the University of Havana who has known Ortega for many years, said the church's defensiveness is a symptom of the difficult role in which it finds itself in a country with no traditional opposition parties or independent institutions.
"The cardinal has insisted the church is not a political party, but in Cuba there are no political alternatives, so like it or not, that is the role the church has assumed," he said.
"To me, it is a political defense of an institution that is preparing to have a role, as far as it is able, in a post-Castro era. They must be very careful with each step."