Dick Sawle, a member of the Falkland Islands Legislative Assembly, said Argentine authorities and agencies had applied increasing pressure on cruise companies not to visit the Falklands for the past two years. The pressure, he said, has included “covert threats” and actions by militants to disrupt business.

In December, for example, Sawle said, a militant group protesting the planned visit of a cruise vessel to the Falkland Islands ransacked the offices of a shipping company in Buenos Aires.

“This action was carried out in broad daylight in the Argentine capital, yet no arrests were made and the Argentine government has made no comment,” Sawle said.

He said the Falklands government “is saddened by the fact that, despite our best efforts, the Argentine government continues to refuse to engage on matters such as this, which are of mutual benefit.”

Many cruise lines are opting to play it safe.

Carnival UK, for example, said it had made “the difficult decision” to stay away from Argentina’s ports in 2013 because of fears that the ships wouldn’t be allowed to enter or would experience delays.

“As a British cruise company we cannot allow ourselves to be the subject of any political dispute or put our customers and crew into any situation where their enjoyment may be compromised,” the company said in a statement.

The British Embassy said a number of other cruise lines had either been refused entry or decided to cancel cruises, including Adonia, Princess, Prestige, Holland America and AIDAcara.

The Argentine government, which calls the Falklands the Malvinas Islands, didn’t respond to repeated requests for comment for this story.

In the past, Argentine officials have said they’re relying on an Argentine law passed in 2010 that requires any ships or vessels traveling from Argentina to the Malvinas Islands to request official authorization from Argentina. The Argentine government contends that it has the right to stop any ship that it believes is exploiting natural resources in its South Atlantic waters.

The dispute has revived the bitterness of the Falklands War in the spring of 1982, when Argentina invaded and occupied the islands until the British government used a naval task force to retake them. The 74-day conflict ended when Argentina surrendered, but not before hundreds were killed.

James Barbour, a spokesman for the British Embassy in Washington, said the Falklands had become increasingly popular for American tourists and other visitors who appreciate their remote location and “quirkiness,” including the colonies of penguins. He said the British government had made it clear to the Argentine government that its aggressive actions were “unacceptable and must stop.”

“The question is really where we go next, whether the cruise companies will reverse their decisions to cancel or whether Argentina will continue to pressure them not to visit the Falklands,” he said.

While the Argentine government is saying little, it’s made its case to the United Nations.

In a September report, the Argentine government said the United Kingdom was “carrying out unilateral activities in the disputed area” by trying to militarize the South Atlantic and exploiting resources there, in violation of a 1976 resolution adopted by the United Nations. The report said the issue of sovereignty was at the heart of the dispute but had yet to be addressed because the United Kingdom had refused to resume negotiations.

In the meantime, people trying to make a living on the islands are caught in the crossfire of the feuding nations.

In the past 20 years, Sawle said, the Falklands have responded to the demand for increased access to the islands by expedition vessels and large cruise ships, which bring in 65,000 passengers each year. He said the dispute had hurt a number of small companies that had invested heavily in facilities and equipment to provide a range of shore-side excursions to visitors.

Kilmartin, who began offering the penguin tours in 2002 as a way to diversify his farm operation, is hoping that the number of visitors begins increasing soon, bringing more business to his Sea Cabbage Cafe and a museum that tells the story of his farm, the 1982 war and life on the Falklands.

He said a visiting ship could easily provide work for as many as 50 people on his farm, including Land Rover drivers, guides, musicians and caterers.

“Ours is one of many small businesses here that are being destroyed,” Kilmartin said.