Would be the discovery of, and implementation of a new form of government. As a pragmatist I know that could never happen.
An unexpected age of enlightenment. How or when this might occur is not foreseeable nor likely. Especially considering the state of education.
Try explaining the oratory of Cicero, the passion of Virgil or the astuteness of Tacitus to the average passer-by on the street. They'd have no idea what you were talking about. Even most academics and politicians would be hard pressed to have any sort of intelligent discourse regarding such topics.
The founding fathers would be well versed in such important matters. Science cannot replace independent thought, vision and wisdom.
There is a sad depletion of critical thinking on all academic fronts.
It's that very critical thinking which is vital to a civilization ascending to a higher level.
When a civilization stagnates, it slowly deteriorates: begins coming apart at the seams.
Colonization of other planetary bodies might also do the trick. It would provide a "new world" which our world now is sorely missing. Perhaps ol' Newt Gingrich wasn't so far off the mark on that one. I'd say this would be the most probable solution, but even still....unlikely.