How might it be argued that the greek polis was destined for failure?

The single greatest political innovation of the ancient Greeks was the establishment of the polis, or "city-state. In the Mycenean age, the Greeks lived in small, war-oriented kingdoms, but for reasons unknown to us, they abandoned their cities and their kingdoms sometime between 1200 and 1100 BC. From that point onwards, they lived in either sedentary or nomadic tribal groups; the period is called the Greek Dark Ages and lasted until sometime between 800 and 700 BC. The tribal or clan units of the dark ages slowly grew into larger political units at the end of this period; beginning around 800 BC, trade began to dramatically accelerate between the peoples of Greece. Marketplaces grew up in Greek villages and communities began to gather together into large defensive units, building fortifications to use in common. On this foundation, the Greek-speaking people who lived on the Greek peninsula, the mainland, and the coast of Asia Minor, developed political units that were centrally based on a single city . These city-states were independent states that controlled a limited amount of territory surrounding the state. The largest of these city-states, for instance, was Sparta, which controlled more than 3000 square miles of surrounding territory. 

The overwhelming characteristic of the city-state was its small size; this allowed for a certain amount of experimentation in its political structure. The age of the city-state in Greece is an age of dynamic and continual experimentation with political structures; this period of experimentation gave the European world most of its available political structures. Its small size also allowed for democracy, since individual city-states were small enough that the free male citizens constituted a body small enough to make policy decisions relatively efficiently. The overwhelming importance of the polis in the evolution of European political structures is betrayed by the word "political" itself: derived from the word polis , "political" etymologically means "of or relating to the polis ." 

Politically, all the Greek city-states began as monarchies. In their earliest stages, they were ruled by a basileus , or hereditary king. The Greeks living in those city-states, however, soon tired of the kings, many of which were overthrown in the eighth century BC. A variety of political alternatives were experimented with in place of the basileus : these included oligarchy, timocracy, tyranny, and democracy.