First, it was Athens, not Greece as a whole. It was free, male descendants of Athenians who were allowed to participate - their degree of whiteness was not an issue independent of that. They had a large class of immigrants and descendants of immigrants who were not allowed to participate.
Most importantly, while there were a few questions settled by referendum where all citizens could vote, most were settled by randomly allotted juries. This meant there was little advantage to forming political parties around popular demagogues, or run well-funded propaganda campaigns.
Athenian democracy got knocked down many times and came back every time, except the last. The second-to-last time, a bunch of immigrants had fought for the liberation and restoration of democracy, and some leaders argued forcefully that they should be awarded citizenship for this. But they didn't get it, the existing citizens voted against.
The reason democracy finally failed was probably this. The Athenians knew (especially the poor) just how unusual and lucky they were to have political freedom, so they were fiercely protective of it - and didn't want to dilute it by sharing it. Eventually a large part of their society had so little stake in democracy that they didn't bother to restore it.
Most importantly, while there were a few questions settled by referendum where all citizens could vote, most were settled by randomly allotted juries. This meant there was little advantage to forming political parties around popular demagogues, or run well-funded propaganda campaigns.
Athenian democracy got knocked down many times and came back every time, except the last. The second-to-last time, a bunch of immigrants had fought for the liberation and restoration of democracy, and some leaders argued forcefully that they should be awarded citizenship for this. But they didn't get it, the existing citizens voted against.
The reason democracy finally failed was probably this. The Athenians knew (especially the poor) just how unusual and lucky they were to have political freedom, so they were fiercely protective of it - and didn't want to dilute it by sharing it. Eventually a large part of their society had so little stake in democracy that they didn't bother to restore it.