The world has taken an even keener interest in Yemen since a botched bid on Christmas Day to blow up a US airliner over Detroit by a Nigerian passenger allegedly trained by the Yemeni-based Al-Qaeda in the Arabian Peninsula (AQAP).
"The world cannot afford Yemen becoming a failed state a la Somalia," said Bruce Riedel, a Brookings Institution analyst who has advised the Obama administration on Yemen and other counter-terrorism issues.
"One failed state on the Gulf of Aden is bad enough," Riedel told AFP.
"Two failed states on the Gulf of Aden with Al-Qaeda operating in both of them would be a very dangerous situation since the Gulf of Aden is where the world's energy resources sail through every day," he said.
Al-Qaeda-inspired Shebab militants control most of Somalia and have been closing in on the Western-backed Transitional Federal Government's Mogadishu quarters.
In Yemen, AQAP "has a robust and resilient capability," Riedel said.
Not only has it staged dozens of attacks in Yemen this year -- mainly on security forces but also on foreigners -- its senior leadership has also withstood Yemeni search-and-destroy missions, Riedel told AFP.
Though its capacity to launch attacks abroad remains unclear, he said, charismatic Yemeni-American cleric Anwar al-Awlaki appears to be a major threat because of his ability to recruit Americans for jihad.
And while Yemeni President Ali Abdullah is focused more than in the past on the threat from the Al-Qaeda affiliate, including the threat to himself and his family, it is still not his top priority, he said.
He said Saleh, whom he calls "a flawed partner" for Washington, is more concerned with a Shiite Muslim rebellion in the north, a secessionist movement in the south, and his and his family's political future.
The best US President Barack Obama's administration can do is manage the tension over their competing priorities and demonstrate that US interest in Yemen goes beyond security to economic and other aid.
Burns's visit sends such a signal, he added.
"It's to send the message... that we want to help this country manage what is going to be a very, very difficult next decade or so as it runs out of oil," faces a massive water shortage, and a ballooning population, Riedel said.
For Christopher Boucek, an analyst with the Washington-based Carnegie Endowment for International Peace, the situation "is getting worse" in Yemen for a combination of reasons.
"It won't be Al-Qaeda that leads to a failed state in Yemen. It will be economic failure, and corruption and governance," Boucek warned.
"We're not going to make more oil, not going to make more water, not going to fix the economy, but there are things you can do across the board to lessen the impact," Boucek told AFP.
"It's what the international community needs to do -- to stabilize Yemen because it's falling apart. And when it falls apart, Yemen's problems aren't staying in Yemen. They're affecting the region, Europe and us," he added.
US aid, he added, is still too focused on military assistance. Washington has also carried out targeted military strikes of its own.
Sarah Philips, a Sydney University lecturer, wrote earlier this year that Washington should continue providing military support to Yemen but avoid an overt US military presence that could cause Sanaa to be branded a US lackey.
In points published by the Carnegie Endowment, Philips, who lived in Yemen for nearly four years, also wrote that Yemen needs to be governed better, more than it needs military intervention or development aid.
"The growth of military jihadism in Yemen stems from the malignancy of the country's political system," said Philips, who called for a "far more inclusive" political system.
Last month in New York, the United States, the European Union and Yemen's Arab neighbors renewed their commitment to the country through a plan for economic development and poverty reduction.
And while some 5.7 billion dollars in aid has been pledged since 2006, more than half of it has not been spent because the Yemeni government so far has not had the capacity to effectively use the funds.
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