In 2004, Gordon Brown estimated a politician’s sell-by date. “Once you’ve had seven years the public start getting sick of you,” he lamented to his aide Damian McBride. Brown had been chancellor since 1997. “You’ve got seven years when you’ve got a chance to get people on board but after that you’re on the down slope.” The time span is disputable but the phenomenon is not. After a certain period, almost all politicians decline.

David Cameron has been Prime Minister for nearly six years and Conservative Party leader for more than ten (only Stanley Baldwin, Winston Churchill and Margaret Thatcher served longer in the 20th century). After a second honeymoon following his election victory last year, he is exhibiting the classic symptoms of decay. His approval ratings are falling, his MPs are rebelling and his mistakes are accumulating. Once the public and the media judge a prime minister to be on a downward trajectory, they become less tolerant of the events and scandals that periodically buffet a government (as Iain Duncan Smith’s resignation, the steel crisis and the Panama Papers have). Every misstep serves as confirmation of political putrefaction.

As the first Conservative leader to win a majority since 1992, Cameron can be aggrieved by his fate. Yet he should not be surprised. Its origins lie in two defining decisions. The first was not to contest a third general election. There was impeccable logic behind this choice. If they have not done so already, prime ministers invariably atrophy after three election victories (as Thatcher and Tony Blair did). Rather than enduring failure, Cameron sought to follow Enoch Powell’s advice to end one’s career “in midstream at a happy juncture”.

His mistake – and Conservative sources have since confirmed that it was one – was to broadcast his intentions publicly. By doing so, he diminished his authority and licensed unending speculation about his successor. Cameron privately compared himself to a US president, constitutionally limited to two fixed terms. In return, like his American equivalents, he has been unavoidably tarred as a “lame duck”.

The second reason for Cameron’s malaise is the EU referendum. His pledge was rationalised as an act of realpolitik to ward off Ukip and appease Tory backbenchers. But it has had the consequences that opponents foretold. It has ruptured the Conservative Party more severely than any issue since the Corn Laws and, as a Tory minister observed, created a “competing centre of authority”. A dissident republic – Brexitannia – has been established in Cameron’s kingdom.

The risk that this struggle ends in defeat for the Prime Minister – and his near-certain resignation – is increasing. As the de facto leader of the Remain campaign, his fortunes are inextricably tied to those of the UK’s EU membership. Labour’s pro-Europeans derive no pleasure from his diminishing popularity. Their Tory counterparts, meanwhile, fear that the opposition is doing too little to reach the left-wing voters whom the Prime Minister cannot.

EU supporters draw consolation from the relative distance of the referendum – 23 June – and the belief that the economic case for remaining will trump all else. If Cameron secures victory, he will have a brief window in which to relaunch his premiership. But such is the animosity engendered by the government’s tactics (such as its £9m pro-EU leaflet campaign) that some Tory MPs say that he could yet face a no confidence vote. “If the foul play goes on, it won’t be hard to get 50 signatures,” a Conservative backbencher told me, referring to the number of names required to trigger a ballot.

All sides acknowledge that to regain authority Cameron will have to share it. The anticipated “unity reshuffle” will include senior cabinet posts for the chief Brexiters Boris Johnson and Michael Gove. Tory MPs, who complain that Cameron’s appointments have long been based on personal preferment rather than “merit”, want a significant reshaping of both the front bench and the Downing Street operation.

If Cameron survives as Prime Minister until his target date of 2019, allies hope that George Osborne, his anointed successor, may revive his wilted fortunes. Having occupied the heights of the Conservative Party for a decade, however, the Chancellor is similarly subject to the forces of decline. The popular assumption among MPs is that the Tory duumvirate, after rising together, will fall together.

Since acknowledging his political mortality a year ago, Cameron has sought to craft his legacy. Before the referendum monopolised his attention, he made a series of thoughtful, well-written speeches on devolution, life chances and prison reform. Conservative strategists emphasised that this was not a bid to colonise “the centre ground” but a reflection of the Prime Minister’s sincerest passions. They spoke of him returning to a project of social renewal that was interrupted by the financial crisis and its aftermath. Even if his reforms bear fruit, the risk is that they will only do so after he has departed office, leaving him with no platform to claim credit.

At present, Cameron’s legacy is markedly inchoate. He has sharply reduced the size and scope of the state but is insufficiently ideological to boast of having done so. His “One Nation” rhetoric has too rarely been accompanied by One Nation policies. With the exception of equal marriage, he has no signature social reform to his name.

If Britain votes to remain in the EU, Cameron will become the first prime minister to have won three referendums – but in no case did he desire the battle. Re-elected and undefeated, he will be recalled as a politician of indisputable skill. But for what purpose were his gifts deployed? The political space for Cameron to provide a better answer than his foes is shrinking.