We all saw from the previous election that Gary Johnson and Hillary Clinton were referred to by their former titles of Governor and Secretary, respectively. Neither one was in office at the time. I know Senators keep the title as well, but most state legislators and officials don’t.
Will Obama still be called Mr. President after Trump takes the oath?
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According to this site, even though it specifically refers to Bill Clinton, no, former Presidents don’t keep the title as a form of address. He would be correctly referred to as The Honorable Barack H. Obama, and in conversation, addressed as Mr. Obama.
There are the formal rules of protocol and there are the customs of everyday speech.
You will never need to know the rules of formal protocol.
The customs of everyday speech say that a person retains the title of the highest office. Not every office sustains its title, though, but there’s no universal agreement on what those are. Pretty much every Judge does, although some judges are so local and minor that they don’t, for example.
You should do a search. We’ve done this topic many times in the past.
What I’ve heard is that you don’t refer to former presidents as “Mr President” because there is only one president at a time. But since there are multiple governors, senators, etc, you can refer to the person as Gov. Clinton or Sen Clinton, and that you should refer to someone by their highest title.
Question: How is the retired Pope addressed?
As to the OP’s question, I agree with EM that there is a lot of disagreement. What I have heard articulated as an attempt at setting forth a rule is that someone keeps the title if his or her office is not unique. There are lots of legislators and judges, so former office-holders from those parts of the government can keep their titles without impinging on the authority of the current office-holders.
There is only ever one President of the US, however, so former office-holders do not retain the title. There are lots of governors and agency secretaries, so they retain their titles in the world at large, but probably would not be referred to by title within their own state or agency, because that would step on the current office-holder’s right to the title.
Bill Clinton is always referred to as President Clinton. George Bush is always referred to as President Bush. Barack Obama will always be referred to as President Obama.
That’s the way our language works today. If you were introducing Bill Clinton at a rally and didn’t call him President Clinton he wouldn’t think “Wow, that guy really knows protocol.” He’d be thinking, “Wow, what a rude jerk.” And he’s be absolutely right to do so.
Look at all these hits for “President Bush” from the last year. His own spokesperson calls him President. And Newsweek captioned a photo with the delightfully confounding “President Bush and Former American Vice President Dick Cheney in the Presidential Limousine.”
Language has moved on. You should join it.
George W Bush’sinauguration speech.
Obama Speech at Bush Center.
So the men holding the office have no problem in refering to their predessessors as “President”. So protocol does not seem to be followed.
Though if Trump calls Obama 'Kenyen" at his inauguration, I would not be surprised. 
I think traditionally in the U.S. ambassadors and judges are also addressed by their former titles.
And Kentucky Colonels 
Actually, when a state governor makes you a colonel (or, in Texas or Nebraska, admiral), it is not a “former” title; it’s a permanent title.
In my state, the title is “Honorary Colonel Aide-de-Camp in the New Mexico Militia”.
“Aide-de-camp” is military jargon for “errand boy”. It does not pay anything, does not entitle you wear uniform, and nobody is required to salute you. You do get a certificate to hang on your mantelpiece.
Not really confounding. Is there really any chance that an audience member doesn’t know that President Bush is not the current president ?
Vice President Cheney consistently was called VP… they added the intro that he is the former VP of some part of the N S pair of continents.