Robert W. Sarnoff, the RCA Corp. heir who for the past two years has served as chairman of Planning Research Corp., has resigned suddenly at a time of continuing financial difficulty for the firm, becoming the third person to leave the post in the past four years.

In a terse statement yesterday, Sarnoff, 63, said he did not seek re-election as chairman when the PRC board met Tuesday, although he remains a director. No successor was named.

"Now that the company's strategic planning process is well along, the operating units restructured and PRC's Washington-area operations consolidated at its new headquarters in McLean, I would like to be relieved of the additional responsibilities I assumed two years ago as chairman," Sarnoff said.

"This will give me more time to devote to some of my other interests," he said, noting that he is president of the National Science Center for Communications and Electronics Foundation and active in the United States Japan Foundation.

A PRC representative would not amplify the statement, and company board members were not available for comment yesterday. Sarnoff, presiding at the company's annual stockholders meeting Tuesday, gave no indication he was about to give up the position. As chairman, he was paid $145,833 and owns 90,000 shares of PRC stock, worth $540,000 at Tuesday's closing price.

Sarnoff became chairman in July 1979, two years after joining the company's board and four years after his ouster from his job as chief executive of RCA, the company his father founded in 1919. At PRC, Sarnoff succeeded Kenneth M. Poovey, who also resigned. Poovey had held the job since 1977, succeeding Harrison A. Price, who quit two months after taking the position.

The company reported a loss of nearly $1.4 million in the 1981 fiscal year, a period plagued by the difficulties of reorganizing a diffuse company into four units and by the costly shutdowns of PRC computer operations in Britain and Southeast Asia.