The shrinking union label in America.

It was 1933. The Great Depression had put a quarter of America's labor force out of work. Late one night, two men - important labor leaders - took a stroll along New York's 55th Street.

They talked about their faltering labor movement. Union ranks had withered in the past 10 years. The younger of the two unionists had a plan to organize workers in newly emerging heavy industries like steel and auto.

But his companion, William Green, president of the craft-oriented American Federation of Labor, hesitated.

''I went to bed, and the next day I began to plan the CIO (Congress of Industrial Organizations),'' John L. Lewis, mineworkers union leader, later recalled. History proved him right. As the new auto and steel industries prospered, so did the labor movement, fueled by the spectacular success of its new industrial unions.

Half a century later, the labor movement is again in crisis. Membership is down. Employers are taking a tougher stance. According to some observers, the time is ripe for a new initiative by organized labor. The union label is becoming noticeably frayed.

Basic industries like farm equipment manufacturers have been slow to recover from the recent recession. The steel industry, in worse shape, is clamoring for protection from foreign competition. Owen Bieber, president of the United Automobile Workers, worries aloud about domestic auto companies moving their plants abroad.

Meanwhile, trade unionists complain, business has taken a harder line with labor. Continental Airlines, which last year filed for bankruptcy, is flying again after replacing union with nonunion workers. In July, Kroger Company threatened to close its 82 Detroit stores unless the union made significant concessions. MCI Communications Corporation has begun hiring replacements for 400 striking workers at one of its subsidiaries.

''The climate out there is anti-worker,'' Mr. Bieber says. ''I blame the President for this. He set the pattern'' with the firing of 12,000 air-traffic controllers in 1981 and the subsequent decertification of their union.

In the face of this onslaught, union membership has stagnated. In 1970, organized labor represented 27.3 percent of the nonfarm work force. One estimate puts the figure at 19 percent now.

Is unionism dying in America?

No, labor experts say, although many go on to forecast a gloomy future for the labor movement.

Within the movement itself, there is more optimism. ''I've always (believed) in the circle concept,'' says Lupe Valadez, an official of Chicago chapter of the United Steelworkers of America. Right now, ''we're at the bottom.''

Organized labor finds itself surrounded by problems. Concession demands from employers, a slow recovery, and presidential politics threaten in the short term. But at least as important is the slow erosion of labor's foundations.

On a bright, breezy September morning, the Kearney & Trecker Corporation - one of the nation's largest machine-tool producers - is showing off its wares.

Inside its large Milwaukee plant, Mark Merk stands next to a display of automated manufacturing systems he installs for the company. A few feet above, a gantry robot, like an overhead crane, moves metal pieces along a predetermined path from machining center to lathe to gauging cell. The process is automatic. It is the latest step in the push toward the fully automated factory.

For workers like young Mr. Merk, the future looks bright. After nine years as a machine-shop apprentice and additional schooling, he has made the transition to his higher-skill job look easy. ''A lot of employees like the challenge,'' he says.

But for John Gruwell, father of four and an 18-year veteran of United States Steel's South Works plant in Chicago, the past looks brighter than the future. He is one of about 1,200 workers laid off from the plant since 1982. Less than 1 ,000 employees are left in the facility that once employed 15,000. And Mr. Gruwell is not hopeful about the future: ''As far as steel goes, I don't think it's going to get any better. You can't compete with the Japanese.''

Although his current job as a hydroblaster pays well, the work isn't steady. Many job listings require skills he doesn't have, he says, waving his hand over the help-wanted section of a local newspaper.

This is what one expert calls ''skill twist.''

In a recent book, Allan Hunt, research manager of the W. E. Upjohn Institute for Employment Research, argues that the robot ''revolution'' is just another step toward automation and won't displace that many jobs in the short term. But workers displaced by the 50,000 to 100,000 robots in operation by 1990 will have a hard time filling the 32,000 to 64,000 new jobs created by the emerging robotics industry.

Like the move to robotics, the much-ballyhooed transition from an industrial to a service-oriented economy is a long, slow process.

Actually, it has already happened, argues Michael Urquhart, an economist with the US Bureau of Labor Statistics. He says the US has had a service economy for some 30 years. Workers haven't had to flee manufacturing, he maintains - their numbers have merely leveled off, while parts of the service sector have continued to boom.

Some labor economists are concerned about ''dein-dustrialization'' - the prospect that employment will decline in manufacturing and other areas of the goods-producing sector. But these fears are premature, Mr. Urquhart says, since the impact of the recent recession on the goods-producing industries may be temporary.

For its part, organized labor finds itself in the same boat as the goods-producing sector. Union membership has leveled off. Observers say labor must reach out and organize private-sector service industries - such as wholesale and retail trade, real estate, finance, and transportation - to keep up with the growing labor force.

''That is one of the major challenges that faces the (labor) movement,'' says Jim Dworkin, industrial relations professor at Purdue University's Krannert Graduate School of Management. ''If unions stay only in that one small slice, their power will be diminished.''

So far, however, union organizing attempts have been unremarkable. For example: Although banks are a target of organizing drives, fewer than 30 in the whole country are unionized.

Why? For one thing, unions would appear to have less incentive to organize service industries rather than manufacturing ones. Since service-sector wages are traditionally lower, unions find it harder to recoup through dues the increasing costs of organizing workers.

''Not all jobs are worth going after,'' explains one union official.

Nor are service workers' potential earnings very high.

''In those old industries like steel, the unions could push for better wages, because productivity was going up so fast,'' says Richard Saunders, associate professor of history at Clemson University. But ''there isn't going to be any great breakthrough in waiting tables, or cutting hair, or teaching schoolchildren.''

Another problem blunting organizing success is what trade unionists perceive as an increasingly hostile environment.

In the 1940s, workers chose to unionize in 8 out of every 10 elections. By 1982, workers chose to unionize in only about 4 out of every 10 elections.

Some unionists blame the most recent declines on President Reagan. They say his appointees to the National Labor Relations Board have tilted it toward a pro-business stance. Others chalk up part of the problem to bad public relations.

''We're a force for good that's portrayed as a force for evil - or for mischief,'' says Alan Kistler, organization and field-service director of the AFL-CIO. ''It's a consequence of a lack of knowledge or contact.''

But Paul Weiler, a Harvard University law professor, has another explanation. In a Harvard Law Review article last year, he argued that the whole process by which workers decide whether or not to unionize is stacked in favor of the employer.

Because of inherent delays, he says, employers have the time and the temptation to use illegal tactics to discourage workers from voting for unionization. From 1957 to 1980, unfair labor practice charges against employers increased 750 percent. In the same period, the number of employees found to be discriminatorily discharged rose 1,000 percent.

Organized labor's future depends in part on the economy. Even under relatively optimistic projections, the US will have a persistent labor surplus through at least 1988, according to an AFL-CIO report last year.

Many observers - such as Bennett Harrison of the Massachusetts Institute of Technology and Barry Bluestone of Boston College - tend to agree. As the number of lower-paying service jobs grows and higher-paying manufacturing and other jobs stagnate or decline, they say, the living standards of a significant portion of the work force may fall.

On the other hand, if the economy expands faster than expected, a shortage of workers could drive up wages and, perhaps, shore up the labor movement.

''The best thing for stiffening the resolve of a union is a labor shortage,'' says Mr. Hunt of the Upjohn Institute.

From 1990 to 1995, the average annual growth of the labor force will be only slightly more than half the rate of the 1970-82 period, according to the Bureau of Labor Statistics.

Women and minorities will play an increasingly important role in that work force.

''Unions must learn to work with the new kind of economy,'' says Jack Howard, assistant to the president of the American Federation of State, County, and Municipal Employees, the membership of which is about 50 percent female.

''Twenty years from now,'' he adds, ''it could be a brand new face on the labor movement.''

The Domestic Policy Association is a nonprofit, nonpartisan group that encourages discussion of public issues, explores alternatives for solving problems, and aims to identify common ground. Those wishing to participate in this year's forums should write to Dr. Jon Rye Kinghorn, Domestic Policy Association, 5335 Far Hills Avenue, Dayton, Ohio 45429, or call (513) 434-7300 for information.