DETROIT — After a prolonged recovery that culminated in two years of record sales, the American auto industry is slowing down, with fewer buyers in dealer showrooms and fewer workers on the factory floor.

Automakers said this week that sales dropped in June for a sixth consecutive month, falling by 3 percent from a year ago, a trend that analysts do not see letting up anytime soon. And as demand falls, there is less work in the nation’s auto-assembly plants — primarily those that build traditional passenger cars.

Last year, those plants hit a peak of 211,000 workers, a 55 percent increase since the depths of the recession in 2009. That figure has dropped by more than 2 percent so far this year, to 206,000 workers in April, according to the Bureau of Labor Statistics, and could shrink further as sales continue to fall.

“There’s been a consistent reduction in plant output in the last six months, and what is ahead in the next six months could be pretty startling,” said Ron Harbour, an auto manufacturing expert at the consulting firm Oliver Wyman.