From the Economist:

Indeed, it is widely believed that some, including Igor Sechin, the deputy chief of staff in the Kremlin and the informal leader of the siloviki, the clan of former KGB men, urged him to make such a change. With little prodding, parliament would have amended the constitution and two-thirds of the country would have supported it. The West, after some grumbling, would have come to terms with it. Deciphering Mr Putin’s real motives is a murky business, as much a matter of psychoanalysis as of political interpretation. It is possible that until recently Mr Putin genuinely wanted to leave the Kremlin and become an international figure bathing in luxury and respect. Staying on might have turned him into a hostage to those seeking to protect their financial interests. As one Yeltsin-era oligarch put it: “You stay for the third term—you may never leave.”