In May 2010, Nelson Mezerhane got the phone call that made him realize he could never return to Venezuela. The then-67-year-old businessman, a co-owner of Globovision, the country’s only independent television network, was in Boca Raton, Fla., where he had taken his family out of concern for their security.

The call was from Hugo Chavez. “Where are you? When are you coming back?” the cau­dillo began, according to an account Mezerhane gave me. Then Chavez got down to business: “I need for you to fix this Globovision. This cannot go on like this. Fix it or take the consequences.”

For nearly six years Mezerhane and his business partner had been under intense pressure to stifle Globovision’s critical coverage of Chavez, or else sell the network. Mezerhane had been imprisoned on bogus charges — the prosecutor who brought them said so before fleeing Venezuela — and he had been publicly accused of everything from plotting to assassinate the president with an F-16 warplane to working for the CIA. But Mezerhane refused to buckle. “Shut it down,” he challenged Chavez over the phone.

Chavez did not do that: His closure of another independent TV station had triggered a huge domestic and international backlash. But a couple of weeks later, his security forces raided and seized Mezerhane’s bank; in August 2010, they invaded his home. That same month, Mezerhane, like thousands of other Venezuelans fleeing the Chavez regime, filed an asylum request in Miami with the Citizenship and Immigration Services office of the Department of Homeland Security. And there our story begins.

Fourteen months later, a man Chavez once described as his No. 1 political enemy has not had a response, nor even an interview, though DHS guidelines provide for a final decision within 180 days. Mezerhane’s attorney, Sandra Grossman, believes his case has been transferred to Citizenship and Immigration headquarters in Washington, where it has disappeared into a bureaucratic black hole along with dozens of other high-profile Venezuelan political asylum cases.

“All of my high-profile cases have been referred to headquarters, where they are just sitting,” Grossman told me. “This is true only of Venezuela. It’s impossible to obtain any information about when they are likely to be adjudicated, impossible to obtain information about why they are still pending.”

Two other immigration attorneys said they have the same problem with prominent Venezuelan clients.

What could explain this logjam? Grossman has a theory: The Obama administration is catering to Chavez. “What’s happening,” she says, “is that for political reasons the government doesn’t want to create a space for Chavez to react when we grant asylum to someone he has labeled a criminal.” The result: “We are leaving deserving applicants and their families in a permanent state of limbo. It creates the image that we are not observing the rule of law.”

Asylum decisions are supposed to be nonpolitical, and DHS officials I spoke to denied that politics has infected the Venezuelan cases. They said that high-profile cases typically take longer to adjudicate because they require more investigation. But Grossman’s theory happens to coincide with Obama administration policy. Under Hillary Rodham Clinton, the State Department sought first to “engage” Chavez and then, when that didn’t work, adopted a strategy of seeking to avoid public scrapes with him, on the theory that he would only use them to rally domestic and regional support.

The price of this policy is borne by Chavez’s victims — journalists, union leaders, businessmen, would-be opposition presidential candidates — whom he persecutes and frequently drives out of Venezuela. The administration rarely speaks up for these beleaguered defenders of human rights and democracy; and when it does, then only at a low level. It has made no effort to hold Chavez accountable at forums like the Organization of American States.

Now it appears to be dragging its feet on helping even those Venezuelans who come to the United States to seek physical protection from the regime. In recent years Venezuela has been one of the largest sources of asylum applicants: It ranked eighth in the world on a DHS list in March. So far in 2011 there have been 670 applications, which can cover families as well as individuals. DHS officials told me that the overall rate of approval for Venezuelan cases has remained constant in recent years. But 135 of 467 cases in 2010 remained open at the end of the year.

Mezerhane says he would like to use his time in the United States to work for change in Venezuela, which has grown steadily more violent and chaotic. For now, however, he and many like him are paralyzed. “It is hard for them to bring their families over,” said Grossman. “They can’t work. They can’t travel. We are effectively silencing them and denying them a platform to voice their opinions.”

Is this really the right way to counter Hugo Chavez?