For us normal people, a Secret or TS clearance is held in abeyance once we leave the Government (or the military), unless it is expressly revoked. Instead, it is inactive, but still attractive to prospective employers who do business with the Government, since it is a lot easier to activate a clearance than it is to start fresh. That's especially true now that it's all done online (as far as the paperwork part) in that e-QIP, or Q-TIp, or whatever that system is.
When the late Mrs. BOP retired, companies were happy that she held a secret clearance, that merely had to be reinstated, as it saved on the cost of them having to do the whole thing from scratch.
I saw it as a COR/TOCOR a few times over a 20+ year period; especially with guys and gals coming out of the military, but even one or two who had held clearances, but had quit the Government, went contractor, and came back to the Government.
I forget, but if I recall (and I'm trying not to), a Secret is good for 10 years, where as a TS is good for 5, correct? I never held a TS, didn't want one, and didn't really need a secret, as far as that goes. None of my contracts required it, and the trend on some of them was to not contain a clause - the one we all saw if we ever looked at a services contract during a re-compete.
Now, having said that, I have no idea whether or not a former President, or any other politician at the national level, has their clearance deactivated when they leave office or not. Then again, how many Congress critters actually leave office. They act like it's a life-time entitlement or something.
Maybe it drops from a TS to a Secret level; that would make sense. On the other hand, if it makes sense, that's not how the Government is gonna do things.
But anyway, let's hear from Caterwauler, who'll tell us how these things really work.