Here are some details on the individual answers:
Die in office - this also applies if Putin doesn't actually die but becomes severely incapacitated and unable to rule while in office (like Salazar).
Lose an election - this implies Putin accepts the results. If he holds on to power, he doesn't cease to become president.
Move to a different position of power - this would mean he maintains significant control of the country/government/security services, e.g. as a Prime Minister, Head of Security Council or some kind of Father of the Nation (like Nazarbayev).
Be overthrown - by anything from a palace coup (think Khrushchev) to a popular uprising.
Leave active politics - if Putin leaves the post of President voluntarily without keeping any significant power (like Yeltsin did).
Feel free to suggest other answers or ask questions in the comments.
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1.00@MaxPayne If he keeps more a less the same power (or gains even more), I'd still consider him to be president, functionally speaking.