This week, Diana Nyad became the first person to swim between the island nation of Cuba and the southern state of Florida without a protective cage, wowing the world. “It's all authentic. It's a great story. You have a dream 35 years ago — doesn't come to fruition, but you move on with life. But it's somewhere back there. Then you turn 60, and your mom just dies, and you're looking for something. And the dream comes waking out of your imagination,” said sixty-four year old Nyad about her feat.

Yet as many impressed Americans stood waiting for her in Key West, Florida, most of these Americans could never stand on the shores of Havana to watch her departure. As part of an American embargo imposed in 1962, most Americans are barred from traveling to Cuba (the ban was allowed to expire by President Jimmy Carter but was re-imposed by President Ronald Reagan).

Over the years, there has been some easing of the travel ban, with President Obama allowing for greater travel by academic, religious, and cultural groups. Yet Obama has chosen to maintain the major features of frozen relations, even once saying that his previous position during his U.S. Senate campaign that the embargo should be ended was simply “eons ago.”

The official explanation behind why there’s a general travel ban and embargo on Cuba is that the United States is protesting Cuba’s human rights record. In 2010, Senator Robert Menendez (D-NJ) complained that normalizing trade and travel with Cuba would “enrich a regime that denies its own people basic human rights,” and even took the step of saying he would filibuster legislation that changed this. But Menendez has also made a point to promote trade with China, which is by most measures at least as much of a violator of human rights as Cuba, if not a greater one. Recall that the United States has no travel ban or embargo not only on China but other major rights abusers like Saudi Arabia and Colombia. In fact, after fifty-one years of the same policy, Cuba’s seen some basic reforms but no major overhaul of its political system that embargo proponents long-predicted.

A more compelling explanation is the power of the domestic Cuba lobby. This lobby, dominated by wealthy expatriates, spends big in U.S. elections. In 2008, the so-called U.S.-Cuba Democracy PAC, for example, spent over a million dollars in American elections, spending slightly less in 2012. Its treasurer is Gus Muchado, a wealthy auto dealer kingpin who resides in the key swing state of Florida. “When it comes to the topic of Cuba, first comes Cuba and then comes the party,” said Sen. Menendez during a gala the PAC put on in 2010.

This pro-embargo lobby also specializes in antagonizing left-wing leaders throughout Latin America. For example, during the 2012 presidential campaign, President Obama rightly noted that Venezuelan leader Hugo Chavez doesn’t pose a serious threat to the United States. Within hours, Connie Mack, the Republican candidate for U.S. Senate from the state of Florida, came out with a terse statement: “Simply put, this President is unfit for duty when it comes to understanding freedom and national security in the Western Hemisphere, and neither are his liberal allies who allow such behavior.”

What Mack didn’t disclose is that his chief of staff and campaign manager, Jeffrey Cohen, worked as a private consultant between 2009 and 2011 and was paid tens of thousands of dollars by anti-Chavez and anti-Latin American left groups.

Although this lobby has enough clout on Capitol Hill to maintain the major features of our Cold War policy towards Cuba, it is losing ground elsewhere. A 2008 poll found that 60 percent of Americans favor restoring full diplomatic relations with the country. And while the Cuba Lobby, losing clout with Democrats like President Obama who’ve taken modest steps to ease the embargo, tries to recruit far-right Republicans like Ted Cruz – who was the top recipient of US Cuba Democracy PAC dollars in 2012 – the most recent election saw Florida’s Cuban-Americans vote in larger numbers for Democrats than Republicans for the first time ever. And while Jay Z and Beyonce’s trip to Cuba this year evoked predictable outrage from Cuba Lobby-friendly lawmakers like Rep. Illeana Ros-Lehtinen (D-FL), it also evinced an outpouring of calls for the end of the travel ban.

Like the rustic old cars lining Havana’s streets, our Cuba policy is a relic of another era, propped up only by millions of dollars by a powerful lobby based in the swing state of Florida. But like those cars, the policy will one day collapse, and a spree of recent signs – as well as the cheers for Nyad on both sides of the straits of Florida – show that the day may be coming soon.