This week the Queen and the Duke of Edinburgh will be out and about as usual. On Wednesday there will be a tour of a Royal Mail delivery office where the couple will be serenaded by a post office choir. Then they’re off to open a bandstand in a local park. The following day there will be a walkabout in Windsor, and in the evening the Queen will light the first of a line of beacons that will create a trail of fire across the country. For, however much they might like to pretend it is just an ordinary occasion, it will not be any routine day, but the Queen’s 90th birthday.

No British monarch has ever lived to be so old. Elizabeth II has also reigned longer than any previous sovereign, outlasting Victoria last September. Victoria only made it to 81 and she was pretty immobile long before the end. The events of this week are designed to send out a very clear message, as showing themselves to their people is what monarchs do, even at the age of 90.

In early June there will be a service of thanksgiving at St Paul’s, a birthday procession on Horse Guards Parade and a lunch for patrons of royal charities in the Mall. The Queen is carrying on, just as she promised in a famous broadcast on her 21st birthday, in 1947: “My whole life, whether it be long or short, shall be devoted to your service.”

The “great imperial family”, which she also promised to serve on that occasion, has long gone, transmogrified into the Commonwealth, and Britain has changed enormously – but throughout it all, the Queen has been there.

As Tommy Lascelles, George VI’s private secretary and the man who actually drafted that speech, observed, she “never spares herself in that exhausting part of royal duty”, and she still doesn’t, decades beyond most people’s retirement age. She is vastly popular, with approval ratings as high as in 1952, a level that most politicians and members of other institutions can only dream about. Even committed republicans hesitate before suggesting she step down.

But should she? How long Elizabeth II can keep going is the unspoken question hovering in the imperturbable minds of her advisers. The A-word – abdication – is taboo in royal circles. “Something you never mention in the Queen’s presence, it would be like saying ‘fuck’ in church,” as one palace official told me when I was researching my recent book on the monarchy. The royal family has still not quite got over the abdication of “Uncle David” – Edward VIII, who mercifully chose his lover over his crown in 1936. It was the worst crisis in the monarchy’s modern history. “How do you think I like taking on a rocking throne and trying to make it steady again?” as his younger brother wrote to him at the time. They certainly don’t want to repeat that experience.

Picture desks are starting to see William as just another middle-aged bald bloke in a suit

These days, though, even popes retire, and it is hard to imagine a queen fast approaching the centenary of her birth and still attending public events. The Duke of Edinburgh will be 95 in June and is not in the best of health. When he is no longer around, will she really want to carry on her duties alone? The form of the next coronation – possibly services across the country as well as the crowning at Westminster Abbey – has already been discussed, and it is inconceivable that abdication is not a contingency plan.

In fact, if the Queen becomes incapacitated in some way, a procedure already exists. Framed in 1937 legislation but originally formulated in the Regency Act, after George III finally went mad in 1811, it allows for the lord chancellor – currently Michael Gove – the Speaker of the Commons, the lord chief justice and the master of the rolls to step in if “by reason of infirmity of mind or body the Sovereign is incapable for the time being of performing the royal functions”. Let’s hope it does not come to that.

The dynasty is assured to the third generation as far as the Queen is concerned. There will be a shortish reign by King Charles III, already nearly 70, who would be the oldest person ever to be crowned. He would be followed by King William V, even now closing in fast on middle age; and then King George VII, who might well reign into the next century if his health is as robust as his great-grandmother’s.

And there lies one of the House of Windsor’s problems: it is actuarial. With ageing monarchs it is difficult to spread the fairy dust on a succession of middle-aged-to-elderly male kings. Camelot it ain’t. While it does not want to repeat the soap opera of the 1990s, future public scenarios can already be mapped out. The media focus is already on who Harry might marry; and then it will shift to where George and his sister Charlotte will go to school, who they are dating, and how they will spend their lives, on an endless loop.

The family will settle for not being too racy. The bourgeois respectability template was successfully developed by Queen Victoria and Prince Albert in the 19th century. But there is a need for a certain level of spectacle to maintain and justify the monarchy’s popularity: what the shy and stuttering George VI called “the high hat business”. Lord Salisbury, Victoria’s future Tory prime minister, noted: “Seclusion is one of the few luxuries in which royal personages may not indulge ... loyalty needs a life of almost unintermitted publicity to sustain it.” When she did eventually venture out, Victoria was pleasantly surprised by the warmth of her reception.

Hence William and Kate’s tour of India, with its heavily symbolic pictures of the couple at the Taj Mahal offering a happier message than when Diana visited alone in 1992. But is it enough? As one royal photographer moaned to me: “Picture desks are already starting to say William is just another middle-aged bald bloke in a suit.” Likewise Kate is seen as too staid and sensible to generate the sort of crowds that Diana did. There has been tabloid criticism of the prince for not undertaking more public duties to relieve pressure on his granny – though he can’t win: if he did not have his job as a helicopter rescue pilot, he’d be criticised for being a useless drone.

The Windsors need to beware another A-word too: arrogance. Both Charles and William tend to be peevish and churlish towards the media, taking them for granted and as being in no need of cultivation. Both may have good reason, given past experience. But it is the petty things that rankle, as when William had to be persuaded to acknowledge, through gritted teeth, even the presence of journalists and photographers accompanying him on an expensive visit to China last year. He eventually gave them a brusque “good morning”.

The British national press is giving up on Charles too, and his worthy invitations to visit organic farms. Charles’s popularity ratings are nowhere near those of his mother, partly because of his all too visible dabbling in contentious issues.

As she enters her 10th decade, the Queen’s public routines are inevitably being reduced, with longer rest periods between events, fewer foreign trips and more careful planning of events. Long to reign over us? The Windsors must hope that it’s true.

• Stephen Bates is the author of Royalty Inc: Britain’s Best-Known Brand, published by Aurum Press