The most visible one is France's stagnant economy and the crisis of the euro, which seems impervious to even Sarkozy's boundless energy.
Yet there are more and more "problems of character" rather than of policy, and these are the ones that seem to be fatal to his hopes of a second term.
Pitching himself as the president who broke with the financial and power corruption of his predecessor, Jacques Chirac, Sarkozy has found his name dragged, directly or indirectly, into several spectacular affairs.
One extraordinarily byzantine scandal deepened last week when police quizzed one of Sarkozy's closest advisers, former Interior Minister Brice Hortefeux.
Hortefeux is reported to have tipped off a friend (and fellow aide to Sarkozy) that he was being probed for lavish kickbacks that went to a presidential election bid in 1995 by former Prime Minister Edouard Balladur. Sarkozy, then Budget Minister, was Balladur's campaign spokesman.
Investigators are determining if these kickbacks were creamed off from "commission" for French arms sales to Pakistan. They also suspect, according to news leaks, that a 2002 bombing in Karachi that killed 11 French engineers - and was officially blamed on Islamists - was revenge by Pakistani officials who had missed out on bribes promised by the French.
Repugnant as this case is, there appears to be little to tie it to Sarkozy.
Yet there's another scandal that, say his enemies, could lead all the way to the Elysee presidential palace.
It concerns allegations in the Le Monde newspaper that billionaire cosmetics heiress Liliane Bettencourt handed out cash-stuffed envelopes to fund the election campaigns of leading conservatives, including Sarkozy's.
France's chief of police, Frederic Pechenard, and the head of domestic intelligence, Bernard Squarcini, as well as a leading public prosecutor reputed to be a close ally of Sarkozy, Philippe Courroye, are to be questioned by an independent investigator. The issue is whether they tried to obtain the phone records of two Le Monde journalists to track down their sources. And, if so, who asked them to do it.
Sarkozy furiously denies any misdoing in any of these affairs. His office says the probes and leaks amount to bias by examining magistrates, who have a wide degree of autonomy under the French judicial system.
"Everyone knows, let's not be naive, the goal naturally is to get Nicolas Sarkozy," Hortefeux said this weekend. "Not half a day goes by without some sort of pseudo-revelations, innuendo, lies and counter-truths."
Even so, beneath the unity of support for Sarkozy in conservative ranks, tiny cracks are starting to appear. After their trouncing in 2007, the Socialists seem to be resurgent and likely to rally around Francois Hollande, a former party chief whose bland demeanour is matched by high public esteem for his honesty.
This is deepening fears within the Union for a Popular Majority (UMP) that Sarkozy's unpopularity is so deep the party may not only lose the all-powerful presidency but also control over the National Assembly.
Sarkozy remains, for now, the logical UMP choice. Supporters say there is time for the economy to turn around and for the Socialists, loyal to tradition, to shoot themselves in the foot.
But behind closed doors, some whisper of a "ditch Sarko" campaign. "There's the smell of an end of regime," the centre-right news weekly Le Point said confidently said last week.
