I can only talk about Sparta as that is my area of expertise. The Spartans conquered Messenia in the 7th Century BC and enslaved the local population who became the Helot (slave) class.

Firstly there were lots of Helot Revolts in Sparta some of them very problematic for the state. The wiki page gives far more detail than I know.

While this may seem like a good thing for the Spartans the reality is that Spartan society became focused around keeping the Helots under control. By the end there were only about 10,000 Homoioi (citizens) compared to 100,000 Helots. The vast slave population allowed the Homoioi to not have to work in the ordinary sense and to concentrate entirely on training for military service which was the only occupation of every Spartan male.

Unfortunately this freedom was wasted as the Spartans were forever concerned with an impending revolt. Critias is supposed to have said that the Spartans 'were at one the most free and the most unfree.' This idea is supported by several sections of Herodotus which I can dig out if you like that essentially outline the spartan military operations which include declaring war on the Helots each year to justify population control and having camps which included watch posts designed to look in for signs of revolt.

Basically this question is based on a misconception that there were no slave revolts. There were but the Spartans put so much effort in to preventing them that very few had significant impact.

According to Moses Finley, Economy and Society in Ancient Greece, which is admittedly dated, the simple reason was that the social and economic structure of most of Greece did not mirror the conditions during the Roman slave revolts. The Greeks, barring the Spartans, which as quantumhovercraft mentioned are a unique circumstance, did not suffer as complete or systematic a breakdown and lack of oversight as during the Roman slave revolts. Similarly, again barring the helots, Greek slaves were largely heterogeneous, increasing the difficulty of organization. Finally, and this should be a very minor point, Greek slaves were rarely initiated in any system comparable to the Roman gladiatorial schools (again barring helots...).

Finley also notes that slave revolts are uniformly uncommon. Even in the American south, slave revolts were rare, at least of such a substantial size as to be worth noting.

I recognize that it is an unsatisfactory answer, but largely the Roman slave revolts took place within a unique set of circumstances in the Late Republic, in which slaves were likely left under-attended, and military and political attention was largely diverted elsewhere.

Note that I am not terribly versed on the subject, and am largely following Finley. I'm sure there are some ancient slavery experts with more recent scholarship around.

As another followup to quantumhovercraft, when Thebes finally defeated Sparta after Sparta had won the Peloponnesian War, one of the first things they did was free the Helots and build a city state for them, so that they could be a local balance to Sparta. (They also took a bunch of small towns and made another city to balance Sparta, and they called it Metropolis.)

So it wasn't quite a revolt, but Sparta was ended as a military power when their slaves were freed. (Which then meant they had no ability to help when Philip of Macedon conquered Greece three decades later).