Workers’ rejection of a union at Amazon.com Inc.’s warehouse in Bessemer, Ala., is a setback to organized labor’s efforts to reverse a decadeslong decline in private-sector membership nationally.

The Alabama result underscores unions’ challenges in increasing membership in the U.S. private sector, where they represent just 6.3% of workers, down from 24.2% in 1973, according to data from Georgia State University.

Hiring at Amazon—the second-largest private employer in the U.S.—and other e-commerce warehouses increased last year even as the country shed millions of jobs, including more than 300,000 union positions, during the pandemic. For unions, the time appeared ripe to organize workers in an expanding sector and an environment where labor unions traditionally have operated: a large blue-collar site where many employees do similar jobs.