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The root cause I think people taking classified documents to the White House and not taking them back. These cabinet secretaries aren't career bureaucrats, so they're learning on the job and picking and choosing which rules to follow. They might even think it's OK to leave classified documents at the White House since that's in the chain of command.
As for the bureaucrats in charge of tracking down the papers after they walked away... I imagine the cabinet secretary's office starts ignoring them soon enough. And what are they going to do, call the White House and say "I need those documents from last week." Yeah, everybody at the White House is busy doing something else. 
In fact, at the White House, some staffer is in charge of keeping the meeting rooms clean. So after one of these big meetings where all sorts of documents get left behind, some staffer throws everything into a box called "president's papers." Eventually the box gets full, sealed and stored where it sits until eventually it goes to the president's home or pool shed. 
My biggest question is... Instead of taking classified papers to the White House, what if they used electronic versions that can be shown on a screen and then disappear after?
I mean, that's accurate, but the only way we're going to actually get something reasonable out of the system is to start prosecuting politicians like you would any other employee, because they're the ones who have the power to change the system.