BRUSSELS — It is by now a familiar, humiliating pattern. European leaders cajole, argue and beg, trying to persuade President Trump to change his mind on a vital issue for the trans-Atlantic alliance. Mr. Trump appears to enjoy the show, dangling them, before ultimately choosing not to listen.

Instead, he demands compliance, seemingly bent on providing just the split with powerful and important allies that China, Iran and Russia would like to exploit.

Such is the case with the efforts to preserve the 2015 Iran nuclear pact. Both the French president, Emmanuel Macron, and the German chancellor, Angela Merkel, made the pilgrimage to Washington to urge Mr. Trump not to scrap the agreement. Their failure is very similar to what happened with the Paris climate accord, and to what is happening now with unilateral American sanctions imposed on steel and aluminum imports, and to Mr. Trump’s decision to move the United States Embassy in Israel to Jerusalem.

And with each breach, it becomes clearer that trans-Atlantic relations are in trouble, and that the options are not good for the United States’ closest European allies.

However angry and humiliated, those allies do not yet seem ready to confront Mr. Trump, wishing to believe that he and his aides can be influenced over time. It is reminiscent of what Samuel Johnson said of second marriages: a triumph of hope over experience.

But there are signs that patience is wearing thin, and that many are searching for solutions as Mr. Trump, in the name of “America First,” creates a vacuum of trans-Atlantic leadership that the Europeans have so far seemed incapable or unwilling to fill.

“The allies are certainly sick of this but don’t seem to have an alternative,” said Jeremy Shapiro, a former career State Department official now at the European Council on Foreign Relations.

“The Europeans are invested down a path of trying to please the president, not out of belief but more hope against hope that they will convince him,” he added. “And they only pursue this at such a level of embarrassment because they don’t have an alternative.”

That is at least for now. After their statement on Tuesday regretting Mr. Trump’s response and promising to work with Iran to preserve the deal, the foreign ministers of Britain, France and Germany are to meet on Monday with Iranian officials “to consider the entire situation,” said the French foreign minister, Jean-Yves Le Drian.

Mr. Le Drian said that the French president, Emmanuel Macron, planned to speak to his Iranian counterpart, Hassan Rouhani, by telephone on Wednesday about “our wish to stay in the agreement,” potentially widening a breach with the Trump administration.

But the real question for the Europeans, Mr. Shapiro said, “is not if they stick with the deal but will they stand up to the American effort to unravel it and take active measures to protect their companies and banks trading in Iran?” That would be “an extremely confrontational stance,” he said, “and it’s not clear that their companies really want that.”

While some think that they should double down on what has now become a pattern — keep talking to Mr. Trump and his aides, hoping to convince them of the need for trans-Atlantic solidarity — others have had enough.

There are increasing voices for rupture. In Britain, Emily Thornberry, the Labour Party spokeswoman on foreign affairs, said on Tuesday that it was time for Europeans to stop “this long and unnecessary indulgence of Donald Trump.”

A senior adviser to the European Union, Nathalie Tocci, said that the Iran deal was a lost cause, because “Trump and Europe have fundamentally different objectives.”

She said that Mr. Trump “is not interested in keeping a nuclear nonproliferation agreement but in regime change in Iran — it’s as simple as that.”

“We have to stop being wimps,” she added.

On climate and trade, on international law, and on the importance of multilateral institutions like the United Nations and the World Trade Organization, the rift with the Trump administration is real, said Ms. Tocci, director of the Italian Institute of International Relations and a close adviser to the European Union foreign policy chief, Federica Mogherini.

“Can’t we defend what our own interests are?” Ms. Tocci asked. “There is something as fundamental at stake here as the trans-Atlantic bond, because Europe can’t exist in a nonmultilateral space,” a world of competing nationalism and protectionism.

“Isn’t it wiser,” she asked, “to temporarily part ways with the Trump administration?” After all, she noted, something similar happened in 2003 over the American-led invasion of Iraq, yet relations were repaired when a new president came along.

Ivo H. Daalder, a former American ambassador to NATO, sees such as break as inevitable. “At some point — after having pushed the Europeans on NATO, Paris, the Jerusalem embassy move, trade and now Iran — the Europeans will come to the conclusion that they’re better off going their own way,” he said. “And that point is rapidly approaching.”

But whatever the mutterings in Berlin, London and Paris, European governments currently show no palpable sign that they are ready to make that sort of separation.

A year ago, Chancellor Angela Merkel of Germany spoke of a more self-reliant Europe, saying: “We have to know that we Europeans must fight for our own future and destiny,” and that “we in Europe have to take our fate into our own hands.” The French have often talked of “strategic autonomy” for Europe.

But little has happened, other than a modest effort by the European Union to improve its efficiency and cooperation in military spending, a program known as Pesco.

The European Union has instead been preoccupied with other dangers — populism, migration, Islamophobia — and the challenge to its values of democracy and rule of law from member states like Hungary and Poland.

On the Iran deal, Britain, France and Germany have already said that they will uphold the terms and will work to keep Iran in the agreement.

To that end, senior officials of the three countries and of the European Union met with an Iranian counterpart in Brussels on Tuesday, before Mr. Trump announced his decision.

European officials are “working on plans to protect the interests of European companies,” Maja Kocijancic, a European Union spokeswoman for foreign affairs, said after the meeting.

That is likely to include euro-based financing for some companies and efforts at legislation to block secondary sanctions from the United States.

But Mr. Shapiro pointed out that European companies feel too vulnerable to risk American sanctions. “What they might lose in Iran is dwarfed by the American market and the reach of the American banking system,” he said.

Ellie Geranmayeh, an Iran expert with the European Council on Foreign Relations, said Europe was “increasingly irrelevant.”

“From Washington’s perspective, the Europeans seem happy to kick the can down the road, which is effectively hollowing out the deal the Europeans spent 10 years trying to conclude,” she said.

If the Europeans “are not willing or able to put more teeth into talks with Washington,” she said, “we risk becoming irrelevant on the political side, too.”

There are also calmer voices, more resigned to adaptation. “Nobody thinks the trans-Atlantic alliance is over,” said Pierre Vimont, a former French ambassador to Washington.

“But how do we make it work with a U.S. leadership that doesn’t want to play the role of leader?” he asked. “How do we move ahead in a world, not without the U.S., but with an American leadership not willing to play its traditional role?”

The hard part for Europe, Mr. Vimont said, would be saving the partnership with Washington while avoiding “the slow drift toward confrontation between Iran and its neighbors and Washington.”

With Europe pushed by the United States to side with Iran on the nuclear deal and to side with China on the trade deal, he said, “it’s going to be very tricky.”