Castro, who has called the base "a dagger plunged into the heart of Cuban soil," famously refused to cash the checks for the lease payment of about $4,000 a year.
President Barack Obama had pledged to close the prison soon after taking office but Congress blocked him from transferring prisoners to U.S. soil and the men still there largely remain in limbo.
Obama may have pledged to close the prison but the U.S. has not announced any plans to give up the base, which is still considered a strategic asset by the U.S. government.
Most Cubans want the base closed, though it also serves a as "a nice piece of anti-U.S. propaganda that's handy" for Castro, said Hansen, a lecturer at Harvard University who is working on a biography of the Cuban leader.
The two soon-to-be-retirees seem uninterested. "We don't get involved in any kind of politics," Henry said. "We follow the laws here and the laws there."
They say neither was asked to spy for either side, though the men have been an important conduit for a community of families of exiles who fled Cuba and were allowed to settle on the base.
La Rosa, whose head comes up to Henry's shoulders and has an easy laugh, said people on both sides of the fence have treated them well. "They make fun of us and say we are communists over here," he said. "And when we get back over there, they say we're imperialists."
Over the years, there has been a steady decline in the number of Cubans working at the base.
As workers aged and retired, the number of commuters dwindled from the hundreds to about 50 people by 1985, according to a base newsletter, the Guantánamo Bay Gazette. By June 2005, it was down to Henry, La Rosa and two others, all earning about $12 an hour, an eye-popping salary by Cuban standards, according to the prison camp's newsletter, The Wire.
Today, most of the work once done by Cubans is performed by workers from Jamaica and the Philippines.
Leaving their homes wearing baseball caps and jackets against the cool Caribbean morning, La Rosa and Henry typically cross the fence-line as the sun rises. They eat breakfast at a house near the perimeter each morning as the military blasts "The Star-Spangled Banner" through loudspeakers.
Then, La Rosa and Henry climb into a blue pickup truck and drive to work through wide streets in a military installation that resembles suburban USA, with sports fields, a school for sailors' kids, a commissary, outdoor cinema and fast food restaurants. The base is home to about 6,000 military personnel, civilians and contractors.
"Sometimes you feel like you are living in two worlds," Henry, a tall, slender man whose ancestors came to Cuba from Jamaica, said at the start of a recent commute. He has worked at the base 62 years. "They are two systems any way you look at it. But we're used to it."
Both Henry and La Rosa say they are looking forward to some rest after decades of what turned out to be an arduous commute.
La Rosa, who has worked on the base for nearly 54 years, said he is grateful for the work, to be able to support his family and also for the recognition from the military for his years of service.
"My co-worker and I, we never expected this," La Rosa said, his voice breaking. "It won't be easy for me to say goodbye to all these people."
Suzette Laboy reported this story Cuba; Ben Fox reported from San Juan, Puerto Rico.