Why did Democracy not last in Ancient Greece?
Basically, because it was unsuited for competition. Greek style democracy demanded intense involvement from the citizen body, and large scale agreement for any important policy or endeavor. Plus, the lack of a developed administrative or fiscal structures was in the way of any large scale developments. These factors made the system suitable for smallish city states, but it could not accommodate expansion of those states, except through a system of alliances and leagues, which worked fine until some members got tired of the leading city’s hegemony. The limits of the system can be seen at work with Classical Athens. They managed very well in uniting Greece against the Persian threat, but once that was gone, they all fell to squabbling, and ended with the Pelopponesian war. Against expanding Imperial states, like Alexander’s Macedonia, or Rome, the too small and disunited city states just folded.