Nobody truly knows what goes on between the vice-president and president of the United States. That’s how they like it, after all. They have a weekly lunch session alone, with no aides and no notes taken.

It’s the ultimate power lunch. They never publicly disagree. The only time they did — over the constitutional amendment to ban gay marriages and civil unions — Cheney got a pass because his daughter is a lesbian, now expecting a child. But the lack of public disagreement has not prevented Washington from constant chatter about the real state of affairs. And the evidence we’re getting is that Cheney is far from the influence he once was.

On two central issues, in fact, he seems to have lost the argument for the time being. Cheney long insisted that no bargain be struck with North Korea over its nuclear programme. But recently the Bush administration did just that — agreeing to provide some fuel oil to the North Korean dictatorship in return for a freeze on new nuclear development. Old nuclear development remains a fact — subject to future negotiation.

What was noteworthy was not just the switch to greater pragmatism in Washington, but the way in which such pragmatism happened. It was secretary of state Condi Rice who saw the chance for a deal and in a call to the president got authorisation to press ahead. Cheney was out of the loop.

In Iraq, the Cheney line is still that the entire war has been a succession of what he calls “enormous successes”. But that is not how the president has described it in recent, far more realistic speeches. And Rice again has achieved a diplomatic advance. Soon, for the first time, the United States will be in a negotiating room discussing Iraq with a representative of the Iranian government.

This is a big deal, as Ahmed Chal-abi, a leading Shi’ite, pointed out in an interview last week. “The mere factor of being present in the same conference room as the Syrians and the Iranians at this level in Baghdad is very significant. I mean, after all, we tried very hard to get this meeting going last year, almost one year ago. But then it was foiled at the last minute.”

This time it wasn’t. The increasing desperation of the Americans is one factor. Widening cracks in Iran’s leadership is another. But the waning influence of Cheney is not to be underestimated.

Cheney has also lost two critical allies. Most dramatically, he has lost Donald Rumsfeld at the Pentagon. Between them, they ensured that most normal channels of sane, government review were effectively bypassed in the Iraq war. They cut Rice out of the picture at the National Security Council and even at the State Department. They were wily bureaucratic infighters able to run rings about a too-trusting president and too-weak outer circle. But that period is very 2003, and Cheney is alone now. He’s especially alone since his key political enforcer and adviser, Scooter Libby, was handed over to the special prosecutor, Patrick Fitzgerald.

The Libby case is a complicated one. The investigation began when the identity of a former CIA undercover agent, Valerie Plame, was exposed in the media by a government leak. The leak was designed to discredit Plame’s husband, Joseph Wilson, who had challenged some aspects of the Bush administration’s case for Iraq’s weapons of mass destruction in The New York Times.

Vice-President Cheney wanted the world to know that he had not sent Wilson to Niger to look into Saddam’s interest in nuclear materials in Africa, and to believe that Wilson got the job because his wife pulled some strings.

Alas, exposing her identity was a potential crime, and Cheney got caught up in the mess. In the investigation, the prosecutor could not find sufficient evidence to prosecute anyone, but did conclude Libby had committed perjury. Hence Libby’s trial for obstructing justice.

The trial itself has become, in some ways, an unflattering exposure of Cheney’s government style, and there are suspicions of criminality. “There is a cloud over the vice-president . . . And that cloud remains because this defendant [Libby] obstructed justice,” Fitzgerald told the jury.

So not only has Cheney lost Rumsfeld and Libby, and lost the argument temporarily over Iraq, Iran and North Korea, he lives under the cloud of the special prosecutor Fitzgerald. The jury has been deliberating for days, and still hasn’t reached a verdict. If Libby is convicted, he could possibly tell Fitzgerald some more. Even if no crime emerges, Cheney’s reputation for “the dark side” of domestic politics will not increase his stature in a White House trying to achieve a kinder, smarter legacy than it has recently garnered.

And yet, the old Cheney endures. Last week he was off to see both President Hamid Karzai of Afghanistan and President Pervez Musharraf of Pakistan, not exactly a low-profile job. His dressing down of Musharraf, who has allowed a new Al-Qaeda base to consolidate in Pakistan near the Afghan border, seemed to have at least one effect. Musharraf arrested a senior Taliban figure within days. But the fact that such a quick result was possible reveals the delicate line Musharraf is walking — doing just enough to prevent a cut-off of American funding, but not too much to prompt an Islamist coup in his own government.

And the fact that after six years of the war on Islamist terror, Al-Qaeda is in the midst of rebuilding a base potentially as dangerous as the Taliban state is not, whatever else you want to call it, an “enormous success”.

Cheney, moreover, is not done with Iran. It’s hard to know what to make of Seymour Hersh’s latest report in The New Yorker on alleged US plans to bomb that country. But nobody doubts that Cheney is the force behind such a contingency.

Back in 2002, he might well have made a decision of this gravity, and Bush might well have gone along. But now: not so much. Congress is against it, the military brass is against it, the State Department is against it, the American public is against it, and Cheney has no Rummy or Libby to guard his back.

But he still has the president. At least we think he does. But only two people really know the answer to that. And they’re not telling anyone.

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