“I never took a cent from the government,” said Mr. Contreras, the Long Island contractor.

The end of protection for his wife, who is from El Salvador, was the first blow to the family of Mr. Contreras, who has become an immigration activist at an organization called Make the Road New York.

The Trump administration says that a program designed to provide temporary, disaster-related help has instead become a quasi-permanent green light for hundreds of thousands of people. It argues that the only criteria the government should consider in continuing the program is whether the original reason for the designation — in this case, devastation from the hurricane — persists.

“Since 1999, conditions in Honduras that resulted from the hurricane have notably improved,” the Homeland Security Department statement said. “Additionally, since the last review of the country’s conditions in October 2016, Honduras has made substantial progress in post-hurricane recovery and reconstruction from the 1998 Hurricane Mitch.”

Critics of the program agree.

“The hurricane was a generation ago, and Honduras long ago reverted to its regular messed-up state, not the special post-hurricane messed-up state required by the T.P.S. statute,” said Mark Krikorian, executive director of the Center for Immigration Studies, which favors curbs on immigration. “There can be no honest basis for an extension.”

The program provides temporary legal status and work permits to people already in the United States, whether they entered legally or not. The Homeland Security secretary decides when a country merits the designation and whether to renew it, if conditions warrant it.

Hondurans have been on tenterhooks since last year, when T.P.S. designation for their country was up for renewal. In November, the government allowed it to automatically extend for six months, citing a need for further assessment.

Among the 86,000 Hondurans who currently have protection under the program, according to the United States Citizenship and Immigration Services, 45,600 re-registered for the six-month extension. An unspecified number out of the total have obtained legal status in the United States, the agency said, and, thus, will not have to leave.