In Singapore -- the first-ever summit between a sitting US president and a North Korean leader -- Kim signed a vaguely-worded deal on denuclearisation, touted by Trump as a historic breakthrough.

But a second meeting in Vietnam in February ended abruptly -- without even a scheduled lunch -- after the two failed to agree on what the North would be willing to give up in exchange for sanctions relief.

The process remains deadlocked and analysts say the two sides have sobered up since.

"Immediately after the Singapore summit, we had a tidal wave of completely unrealistic, almost comical expectations," said Andrei Lankov, a professor at Kookmin University in Seoul.

"Then it became clear what has been obvious -- the North Koreans are not going to surrender nuclear weapons," Lankov told AFP.

Kim declared an end to nuclear tests and long-range missile launches last year amid a rapid rapprochement, paving the way for the Singapore meeting.

Since Hanoi, Pyongyang has accused Washington of acting in "bad faith" and given it until the end of the year to change its approach.

And last month the North fired short-range missiles for the first time since November 2017.

"We have gone from what felt like a spirit of hope and optimism to now a clear path of uncertainty," said Harry Kazianis of the Center for the National Interest.

- 'Military and diplomatic surrender' -

US officials say privately there has been no direct contact with the North Koreans since the Hanoi summit and have expressed increasing frustration over Pyongyang's silence.

The North has instead spoken through its state media, demanding the removal of Trump's top aides -- Secretary of State Mike Pompeo and National Security Adviser John Bolton -- and warning of a "new path" if Washington does not change course.

The two leaders went to Hanoi with very different approaches -- the US wanting an "all-for-all" deal while Pyongyang sought a "step-by-step" process -- and have blamed each other for the failure to reach an agreement.

Washington accused Pyongyang of effectively demanding an end to all sanctions for partial disarmament, while the North said it wanted some of the measures eased in return for closing all the nuclear production facilities at its Yongbyon complex.

"The current impasse will continue indefinitely unless both sides can come to grips with why it has occurred in the first place," Kazianis told AFP.

In Hanoi the US had in essence demanded "an unprecedented military and diplomatic surrender" by Pyongyang, he said, but added the North should not expect "the most crippling sanctions" to be removed for only closing the Yongbyon facility.

The two leaders will drag out the current stalemate "to prevent engagement from running completely off the rails", the Eurasia Group said in a brief, forecasting a slight possibility of a third summit this year.

- 'Cycle of provocation' -

Officials in Washington say they have proposed working-level talks to Pyongyang but are not planning another summit until a deal is hammered out.

And with a US president who says he is in "no rush" and appears content with the status quo, analysts say the ball is now in North Korea's court -- even as Pyongyang insists otherwise.

Trump has dismissed worries about the North's recent missile tests, reiterating his trust in Kim who he described as "a man who perhaps wants to get attention".

With sanctions still in place, the US expected pressure to mount on the North to offer concessions, said Go Myong-hyun, an analyst at the Asan Institute for Policy Studies.

But Go warned that Pyongyang appeared to be "heading back towards its traditional cycle of provocation".

The missile launches were "a friendly reminder to Donald Trump that North Korea exists and that they still are ready to talk", Lankov said, adding the North had been "explicit" about resuming nuclear testing unless the US accepts its conditions.

But even if the two mercurial leaders returned to the talks table for a third time, Lankov said, any compromise would be "very difficult to negotiate".

"The Americans are not going to accept a nuclear North Korea and North Koreans are not going to live without nukes."