On Sept. 30, 1976, the Renegotiation Board, a 27-year-old federal agency that reviews federal contracts and recovers excessive profits from contractors, lost its legal authority to review contracts and recover profits.

Logic might dictate that the board, having lost the power to perform its sole functions, would cease to exist. Instead, the tiny agency has displayed a tenacious ability to cling to what life it has left.

The board's staff is about the same size it was when the statue authorizing its operations expired 18 months ago. The agency has just issued new regulations that expand its jurisdiction considerably. And last month it asked Congress for a 15 percent budget increase - to $7.3 million - for fiscal year 1979.

The legal explanation for the agency's continued existence is that it is still plowing through a backlog of work that built up before its authority terminated. (The board's staff, which could be out of work when the backlog is completed, reports that it is making little progress in disposing of backed-up contracts.)

But the deeper reason for the agency's extended lease on life is political.

The Renegotiation Borad has some powerful friends, including Jimmy Carter, Ad. H.G. Rickover and Sen. William Proxmire (D-Wis). They want it kept alive until they can win congressional support for proposals that would make the board a permanent agency and strengthen its ability to recapture profits.

The board was created on a temporary basis during the Korean War as a check against profiteering by arms suppliers during the rapid buildup for that conflict.

At regular intervals over the next quarter-century Congress extended the board's "temporary" authority. The last extension expired on Sept. 30, 1976. Efforts to pass another temporary extension thereafter faltered due to a stalemate between two opposing forces in Congress.

One group, led by Proxmire and Rep. Joseph G. Minish (D-N.J.), and backed by Carter and Rickover, was pushing for legislation that would give the board permanent status, a larger staff and various auditing tools to enhance its watchdog role.

But an opposing faction, composed of Republicans and Democrats from states with heavy concentrations of government contractors, pushed an opposing bill that would have closed down the board, leaving it in mothballs except in times of national emergency.

The agency's suporters say it provides esssential protection for the government on defense and space equipment purchases, where the normal price-controlling pressures of a competitive market generally do not exist. Opponents see it as just another generator of government red tape that adds more to the cost of government work than it saves in profit recoveries.

Since neither faction is sure it has the votes to prevail in Congress, the matter has stayed at dead center for two years. Meanwhile, the board has been permitted to live on, plugging away at the backlog and seeking everlarger annual budgets, which are necessary, it says, to accelerate disposition of pending work.

But now the pattern might be due for a change. The House Appropriations subcommittee that funds the board says it has had enough.

"This thing could go on forever," complains Rep. John Slack (D-W.Va.), the subcommittee chairman.

"You know, they don't even have any authorization," Slack says with consternation. "I'll grant you, they probably have an authorization by next year, we might just tell them to close up."

The normally mild-mannered Slack was particularly exercised to learn that the board this year issued regulations giving itself authority over American firms' sales to foreign governments - jurisdiction that was never explicit even when the authorizing statue was in effect.

"I don't see where they have the power," Slack says. "I mean, they're not even authorized to review contracts with our own government anymore."

At the board, meanwhile, Chairman Goodwin Chase views the lack of authorizing legislation as a temporary embarrassment, Chase says he is "hopeful" that Congress will soon give the board the power to perform its functions again.