On Air Force One on Thursday afternoon President Obama’s press secretary walked down the plane to talk to the press. The first question put to him, by an American reporter, in the middle of a momentous week dominated by Mr Obama himself and by Chinese, Russians and Iranians at the UN, was: “Gordon Brown — are we snubbing him? And if not, why did we turn down five requests for bilaterals?”

Robert Gibbs replied: “The notion that there remains anything other than a special relationship between the two countries is silly and absurd. The President spoke with Prime Minister Brown on the phone in the lead-up to G20 just two weeks ago. They spent time after the climate change dinner on Monday. They spent time after the Security Council today … I think this is a media-generated bunch of silliness.”

Silly or not, the President changed his schedule at short notice yesterday to allow the one-on-one meeting that Downing Street had been pushing for all week – and it was not to placate the media, it was to placate Mr Brown.

It is nearly eight years since Tony Blair won a resounding ovation after telling both houses of Congress that Britain stood shoulder to shoulder with America after the 9/11 attacks.

In those eight years Britain has been by far the largest contributor of combat troops, intelligence and logistical support, after America, to two American wars of choice, one of which President Obama still considers a “war of necessity”.

In the days before this G20 summit, Gordon Brown’s staff repeatedly sought a one-on-one meeting with Mr Obama to discuss shared priorities — from defeating al-Qaeda to rebalancing the world economy, a subject on which Mr Brown is widely considered an expert — and, frankly, as a quid pro quo for his solidarity.

Five times they were turned down. The Russian, Chinese and Japanese leaders all had bilaterals, but the Prime Minister has made do with a hurried conversation at a kitchen table and a presidential hand on his shoulder after yesterday’s meeting of the UN Security Council. He also had a photo call with the President before dinner last night, as did every other guest.

Both sides insist that nothing is amiss with a relationship forged in two world wars and nurtured for half a century by close personal ties between most occupants of Downing Street and the Oval Office. British officials protest almost as vehemently as Mr Gibbs that concerns about the health of the special relationship are a peculiar neurosis of reporters in search of a story. Yet, relative to history, something is amiss. The relationship still exists. It is just no longer special.

Three factors have left Mr Brown in the undignified position of seeming to crave attention and being denied it. His acquiescence in the release of Abdul Baset Ali al-Megrahi, the convicted Lockerbie bomber, enraged the Obama Administration to the point that the President raised it in a recent phone call to Downing Street and allowed Mr Gibbs to note the fact in a summary of the call.

Mr Brown has also found himself on the unfashionable side of the intensifying debate on Afghanistan: he has endorsed General Stanley McChrystal’s call for a manpower-intensive new strategy based on defending civilians and has offered yet more British troops — while Mr Obama wonders whether to tear up the McChrystal plan and think again.

More important than either, Mr Obama is not sentimental. If he were, there might be a new special relationship with Kenya. Instead there are new understandings, emerging almost daily, based on pragmatism and need. Mr Obama needed to sit down with Mr Medvedev to nudge him to reciprocate for scrapping a land-based European missile shield. He needed to sit down with the Chinese and Japanese leaders because one is new in post and both are vital to his goal of rebalancing the world economy.

He needs Britain, too, but until yesterday the need was not quite urgent enough, nor the clamour quite loud enough, to force him to earmark time. Mr Brown has now had his meeting with the world's only political superstar. It may be a while before he has another. If so, he can console himself with the idea that the ties between the two countries are so strong that neither has much left to prove to the other? He may have to.

He needs Britain, too, but the need is not quite urgent enough to force him to earmark time, and he may find the Prime Minister hard to connect with on a personal level. That might change if the Prime Minister changes, or if Mr Obama matures as a statesman. In the meantime the question for Mr Brown is whether he can take consolation in being taken for granted. Can he accept the idea that the ties between the two countries are so strong that neither has much left to prove to the other? He may have to.

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