I believe this action is part of a broader effort by the President to keep any unscrupulous elements away from national security secrets. Sorry, there is no First Amendment right to have access to national security secrets.
Here's apparently how security clearance for ex-CIA Directors normally works. 
Also, ex-CIA Directors are allowed to retain security clearance NOT for their convenience, but for government's convenience, because government may need to tap into their expertise.
President seems to have determined Brennan's services are no longer required. He has done quite enough damage already. Clearly the President's call to make. And if John's services are ever again required, he can of course be given security clearance then. End of story.
By the way, when it comes to matters of national security, "generally living in a manner above reproach" involves Caeser's wife standard, i.e. one must not only be chaste but must also be seen/perceived to be chaste.
I would humbly submit that John Brennan perjuring himself in a Congressional hearing, and taking daily partisan potshots, and being employed by a network demonstrably hostile to a sitting President, clearly violates the standard of behavior that is above reproach.
Here's more on what kind of a person John Brennan is.
