Like all political leaders, Angela Merkel has a dusty room where she deposits unwanted gifts from visiting dignitaries. Unlike other leaders, however, the German chancellor also maintains a dark corner of her mind where she banishes unwanted labels.

At postunification Germany’s cabinet table in 1990, Helmut Kohl patronised her as his Mädchen. The media has dubbed her the Iron Chancellor for turning a 2005 election near-defeat into victory; later she was Madame Non for refusing to write euro-crisis blank cheques for others’ budgetary black holes.

Waving goodbye to President Barack Obama in Berlin yesterday, the 62-year-old now has a new label pinned to her back that Donald Trump’s imminent arrival makes difficult to unpick. All hail Angela Merkel: leader of the liberal free world.

Others might be flattered by this designation, but Merkel, her aides say, is particularly dismissive of this latest label.

They say it says more about the sorry state of the other big western powers than it does about Merkel: the US is in pre-Trump limbo while, in Europe, Britain busks its way to the Brexit door, France is on far-right watch, Italy faces a make-or-break constitutional referendum, and Spain just limps along.

As her peers struggle to survive, Merkel seems to thrive on several fronts: containing fires on Europe’s fringes, from Ukraine to Syria, while keeping the home fires burning. And all with the unhurried air of a drifting iceberg in a trouser suit.

Mulling the secret of Merkel’s ongoing success, the weekly Die Zeit put it best this week: “You never have the impression that she has anything better to do . . . Being chancellor is, for Merkel, not a job or a calling but a state of being.”

The question is: for how much longer? In the next fortnight, possibly as soon as tomorrow, Merkel will announce whether she wants, as most people expect, to run for a fourth term next year. But has she any choice?

In many ways Merkel embodies continuity and common sense lacking elsewhere, reflected in her remarkable 52 per cent popularity rating – just below her rating on taking power in 2005.

Look beneath the surface, though, and there are serious signs of wear and tear. Her Christian Democrats are almost 10 points down on their 2013 election result. Despite steady growth and a record low jobless rate, populists in Germany are on the rise.

As in the EU and US, German populists are both catering to and catalysing unease about the cost of globalisation, the risks of refugees, and the threat of terrorism. And in Germany, as elsewhere, the mainstream political response to voter frustrations has been all diagnosis and no prescription.

Merkel said on Thursday that globalisation requires a “human face” but kept to herself how, in concrete terms, she plans to do this in the final year of her third term, which, in political reality, is actually just six months.

Her grand coalition will down tools for good ahead of next May’s election in the sprawling state of North Rhine-Westphalia, home to one in five Germans. For many this is still a thriving industrial heartland; for millions of others, in cities like Duisburg and Gelsenkirchen, shuttered coal mines and empty factories have robbed them of an identity, an existence and a certain future.

With high unemployment, crumbling infrastructure and a high non-German population, North Rhine-Westphalia offers clear parallels to the regions that embraced Brexit and Trump. An already ambivalent mood here to Merkel is one big Islamist attack away from collapse, triggering a domino effect through to September’s federal election.

Waiting to scoop up disaffected voters – and activate frustrated nonvoters – is the populist Alternative für Deutschland. It sits in half of Germany’s state parliaments, is polling 13 per cent nationally and is poised for a Bundestag debut that will disrupt existing coalition arithmetic. Its deputy leader, Beatrix von Storch, says that Merkel’s renewed candidacy is a gift for them but says, “in the interest of our country, that’s something I’d be happy to do without”. “Angela Merkel is not the hope for the western world,” she says, “but risks being the nail in its coffin.”

With the AfD on her back, Merkel knows that next year will be a very different election race from last time, with cyberhackers and postfactual spin influencing the social-media feeds where millions of Germans now inform themselves.

The irony is that Angela Merkel’s indispensability, in Germany and beyond, is largely of her own making. Early on as leader of the centre-right Christian Democrats she sidelined all would-be challengers. Failing to build up an obvious successor since then, critics say, has left her hostage to her party’s fortunes. And without her the Christian Democrats have nothing.

The party’s staggering leadership crisis was clear this week when the chancellor was forced to back Frank Walter Steinmeier, her foreign minister from her Social Democrat grand coalition partner, as Germany’s next president.

Similarly, at EU level, Merkel is both strong and weak. Berlin flexed its muscles as the chief underwriter of the euro crisis, but the limits of Merkel’s EU influence were exposed when she tried and failed to secure a burden-sharing refugee crisis.

Her plan B, a refugee-swap deal with Turkey, has left her dangerously dependent on an erratic leader with dictatorial ambitions.

For 11 years Merkel has operated on full throttle, but now the question is which runs out first: her reserves of energy, to keep going, or the cast of EU countries willing to step up and be counted on pressing issues like defence and security in Europe if, as likely, a Trump administration steps back.

In Berlin’s chancellery on Thursday evening the hour-long Obama-Merkel press conference was heavy with end-of-an-era nostalgia. That Obama found three days for the German leader, with talks bookended by two dinners, added a passing-the-torch quality to his long European goodbye.

The German leader’s next major hosting duty comes next July, in Hamburg. As G20 president she will welcome President Trump and, if French and Dutch voters so wish, the far-right leaders Marine Le Pen and Geert Wilders.

Faced with that scenario, it is cold comfort to Angela Merkel that, of the western world’s old guard, the last man standing is a put-upon woman.