Government officials say he's recovering, but many people now suspect something's going on. The Algerian and French media are saying the 76-year-old president's health is deteriorating and there are rumors he's dead.
These concerns have deepened in recent days after Algerian authorities closed down two Algerian dailies that quoted French medical sources as saying Bouteflika was in a coma in the Val de Grace Hospital in Paris where he was flown after his reported stroke.
Prime Minister Abdelmalek Sellal sought to quell the rumors and broke the official silence on Bouteflika May 20, saying the president was "never in danger," and was convalescing well in Paris.
"I would like to reassure our compatriots on the state of health of the president of the republic," Sellal announced. "His health is improving day by day."
But Algerians remain perplexed and suspicious of the leadership in advance of presidential elections scheduled for April 2014.
Abderrazzak Mukri, leader of the main Islamist party, demanded May 20 that Bouteflika be shown on television to prove he's alive, and if he didn't appear soon the government should use constitutional powers to remove him on health grounds.
The elections will be critical for the energy-rich state amid the political upheaval convulsing North Africa, the swelling threat from jihadists and a generational change in a security-heavy nation desperately in need of new blood at the top.
Bouteflika, elected president in April 1999, was last seen in public April 17 at the funeral of a high-ranking official.
Given the president's health problems, it seems a pretty safe bet he won't be running for an unprecedented fourth term in April. He's the last of the generation that won Algerian independence from France in a 1954-62 war and his rivals are all much younger. They include Sellal, who's 64.
Another potential candidate is former Prime Minister Ahmed Ouyahia, 60, leader of the National Democratic Party, which is the junior partner in a longtime coalition with Bouteflika's National Liberation Front, the party that led the fight for independence.
Algeria's military chiefs, who reportedly favor Ouyahia, have largely ruled the country since they cancelled 1992 elections the Islamists were set to win, triggering a decade of war.
They're concerned the country faces a major security threat from al-Qaida of the Islamic Maghreb and its allies who are expanding their operations across the region.
Algeria has the region's largest and most effective military, and intelligence service.
But it's been reluctant to cooperate with neighboring powers, such as Morocco and Egypt, let alone the United States and France, to fight AQIM.
The last thing they want is another religious conflict like the 1992-2002 civil war in which more than 150,000 people were killed.
That attitude may have changed following a pulverizing attack by a 40-strong jihadist unit that seized the sprawling In Amenas natural gas complex in Algeria's southeastern desert in January.
The army stormed the complex, killing nearly all the attackers along with 37 foreign technicians.
Many saw that as a wake-up call. Algeria can no longer afford to stand by as the region becomes a major battlefront in the struggle against militant Islam.
Algeria calls itself a democracy but it's essentially run by the generals, collectively known as Le Pouvoir, The Power, a shadowy cabal that these days is dominated by the DSR intelligence service headed by Gen. Mohamed "Tewfik" Mediene, who has been working to undermine Bouteflika for years.
The state energy giant, Sonatrach, a longtime Bouteflika bastion, has been a particular DRS target. Mediene arrested the top managers, all Bouteflika's people, on corruption charges. Bouteflika was powerless to stop him.
That move was hailed by many of Algeria's 35 million people, disgruntled by state corruption, poverty, high unemployment and poor housing despite the country's energy wealth.
The leadership has used oil and gas revenues -- Algeria exported $73 billion in petroleum products in 2011 -- to buy off discontent.
But OPEC figures show Algeria's oil production fell in 2011 for the fourth consecutive year, from 1.37 million barrels a day in 2007 to 1.16 million bpd.