Not a historian but I could argue that Athenian democracy succeeded despite itself. It gave significant power to a segment of the population that was usually ignored but the assembly would then go on to make some horrible decisions.

Firstly I would note that Marathon was in 490 BCE but was forever be looked at as the ideal for the conservative elements (i.e. elites) who despaired about Athens being ruled by demagogues and the mob. Marathon was a victory by the landowning segment of the population (and historians like van Wees argue was dominated by people who owned enough land and slaves to never need to work it themselves), when the hoplites dominated politics rather than the lower-class navy. Democracy looked instead to Salamis which was won by the (primarily) lower class navy.

The Athenian democracy, while revolutionary in the power it gave to the ordinary citizen, still had some problems. It was dominated by those who lived near the city - if you were a poor farmer who lived a day away then you rarely (if ever) would get to the Pnyx to vote. So it would be dominated by people who lived in the city or the immediate vicinity. Secondly it was dominated by demagogues - usually elite men (or 'new men' such as the often bashed Cleon) in the office of strategoi. These men would have been trained from birth to lead, have the training in rhetoric to be able to speak pleasingly (and probably the voice training to communicate clearly to thousands of people without a microphone). While any individual could technically stand up at the assembly and make a speech - can you imagine yourself standing up among 6,000 of your neighbours and citizens and after a trained speaker, it would take considerable stones to do that.

So yes, the Athenian democracy was an incredible thing (and one could argue more democratic than our system today were we cede our decision making capability to some schmuck we elect every 4-5 years and hope they do what we want) giving each citizen the right to decide on every facet of the state: do we make war, or peace, or send ambassadors to Persia?

Now the dark side of Athenian democracy - it was tempestuous and schizophrenic. The assembly voted to send a massive expedition on the doomed Sicilian Expedition (egged on by demagogues who said it'd be easy) which wiped out Athens' navy and army. The assembly voted to execute all males (and sell off the women and children) of the rebellious Mytilenes and sent off a ship with that order, on the following day they reconsidered and immediately sent off a second ship to countermand the previous order and only execute the ringleaders. Later in the Peloponnessian War when another revolt occurred, the assembly voted to execute the men and enslave the women and children of Melos - and there would be no reconsidering this time (late in the war and Athens was much more desperate).

What shows the turbulent nature of Athens democracy is best shown by the reaction after the naval battle at Arginusae. After the Scilian Expedition had failed and Athens entire fleet was destroyed, the city used emergency funds (including raiding their own temples) to build up a new fleet and they defeated the Spartan navy in a key battle at Arginusae. Unfortunately a storm blew up after the battle and prevented the Athenians from recovering survivors or the dead - and lack of a proper burial was not a good thing. So when the strategoi (admirals/generals) returned they were prosecuted. However the generals managed to explain why they failed to recover the dead/survivors and were let off. Then a little later at a religious festivals, the dead sailors came up again and emotions got heated and the strategoi were again prosecuted, found guilty, and executed. Then a few days later when things had cooled down, the assembly went after the man who had pushed for the executions. Worse, the executions of so many experienced leaders left newer and inexperienced strategoi in charge who contributed to the destruction of the Athenian navy a little while later at Aegospotami.

This was the Athenian democracy, warts and all.

Edit: I should have added something that explained a bit about how the democracy lasted so long from the elite perspective. Democracy was another system of government that developed due to the constant competition for power and dominance among elites. Ancient Greece being a very agonist society, your standing only rose if somebody else's fell. So elites were constantly fighting for power which caused considerable unrest. Things like oligarchies were solutions to this problem. Athenian democracy succeeded because they channeled that elite competitive drive into other areas.

There was still the office of strategos that they could be elected to repeatedly. There was also the courts where elites could compete against each other through lawsuits and accusations. But also liturgies like the theatre: elites competed as the best playwright in comedy or tragedy, or as the best choregos (producer) for the best play. It was a brilliant system, to harness all that competitive drive and funnel it away, thus protecting the democracy (though aristocratic coups did occur from time to time).