Fairfax County Executive Leonard L. Whorton was summoned by his bosses - the Board of Supervisors - for a two-hour fault-finding session this week.

According to board Vice Chairman Martha V. Pennino (D-Centreville), who called the closed meeting, a majority of the supervisors criticized Whorton's performance at the meeting. None of the supervisors called for Whorton's resignation from the $49,000-a-year position he has held since August 1976, she said.

"I think it is fair to say that a majority feel the county executive is not a strong executive," Pennino said.

According to another supervisor, who asked not to be named, seven of the nine members of the board had complaints "that were fairly significant." Most of the complaints seemed to fall in three categories: (1) that Whorton was no assertive enough, (2) that he had not succeeded in reorganizing the bureaucracy to make it more responsive and (3) that he had poor communication with the board and even with his own departments.

Historically, Fairfax's county executives have had an uneasy, sometimes tumultuous relationship with the supervisors. George J. Kelley Jr. resigned abruptly in the middle of the board meeting 5 1/2 years ago. His successor, Robert W. Wilson, quit 2 1/2 years ago after an election wiped out the liberal majority with which he had worked closely. J. Hamilton Lambert, who was named acting executive after Wilson, let it be known that he did not want the job permanently.

The source of much of the friction, Pennino and some other supervisors said, is the county's peculiar structure of government. Though he is expected to manage the government full time, the county executive has no policy-making powers, and cannot even name deputies without board approval.

Furthermore, unlike his counterparts in suburban Maryland, he is not elected. He is appointed by the supervisors, and serves at their pleasure.

"You have to be a darn clever toe dancer" to survive, Pennino said.The Tuesday session did not resolve Whorton's future, she said. He will face more evaluations in the future, she said.

Some of the supervisors willing to talk about the Tuesday meeting defended Whorton. "I wanted someone who would be moderate and straight-forward - and Whorton has been that . . .," said Audrey Moore (A-Annandale). "The Monday session was bear baiting."

Board Chairman John F. Herrity, a Republican said: "I think Leonard Whorton is doing a good job, which doesn't mean there aren't problems." Pennino and Herrity said the office of county executive may have to be made elective to eliminate some of the recurring difficulties.

Whorton, who was hired after a nine-month search, came from Richmond, where he had served as assistant city manager. He brought to Fairfax a reputation as a professional administrator who stayed out of politics.

But with the board divided into several factions - each trying to enlist his support - Whorton has found that his neutrality did not make him immune from attack. In recent board sessions, some board members, unhappy with his recommendations, have publicly criticized him.