Although New York City may have been in an economic recovery for the last five years, it continues to lose jobs at a rapid pace in one key area: corporate headquarters.

According to the Bureau of Labor Statistics, "Employment in administrative offices of manufacturing companies declined by 3,500 in 1980, the sharpest drop in five years." In 1979, New York City lost 3,200 front-office manufacturing jobs.

By the end of 1980, "Employment in the headquarters sector of the New York economy was down 41 percent [to 50,900] from its 1969 peak of 86,000," Samuel M. Ehrenhalt, regional commissioner of the BLS, said today.

In the last four years, when the number of jobs in the nation's biggest city increased by 117,000, the number of jobs in the headquarters of manufacturing companies fell by 8,300.

The Labor Department keeps statistics only on headquarters of manufacturing companies. It is unknown whether jobs at the home offices of other types of companies, such as retailers, have increased.

Ehrenhaft said the continued weakness "in the city's ability to hold and attract headquarters office jobs is of concern for its economic development and its national economic image. These headquarters jobs are significant for the city's economic vitality beyond the immediate numbers involved. The administrative-office sector generates economic activity in a number of the city's important employment sectors including finance, communications, transportation, advertising and other business service industries."

But New York remains the nation's city with the most corporate headquarters. It is followed by Chicago, although Fairfield County in Connecticut, a New York suburban area, has more corporate headquarters than Chicago.

A number of major corporations have fled New York City in recent years, most of them to suburbs in Connecticut or New York, Ehernhaft noted in a speech to the New York City Council on Economic Education that in "contrast to the last year's loss in New York City . . . in the five neighboring suburban counties of Nassau, Suffolk, Westchester, Rockland and Putnam, employment in the administrative offices of manufacturing companies inched up by 200 after rising by 1,800 in the prior year."

During the last four years, when New York City lost 8,300 front-office jobs, the five neighboring counties added 4,400.

City officials such as the ebullient Mayor Edward Koch have made much of New York's economic revival in the last several years. As in several other major American cities such as Chicago, a construction boom is under way in midtown Manhattan. At the same time, studies show that many New York residents and office workers feel that the quality of life in New York is declining, in large part because of budget constraints.

New York City, for example, has its economic house in enough order to sell bonds for the first time on its own since 1975. At the same time, its subway service is deteriorating for lack of funds, the streets are dirtier than a decade ago because of layoffs in the sanitation department, public hospitals have been closed and the number of police on the streets has been reduced.