At the risk of sounding flippant, because the Athenians wouldn't let them? It wouldn't be much of an empire if subject states could just leave at will, would it? It seems a bit like asking why a victim of robbery doesn't just walk away with a gun pointed at his or her head.

More seriously, some cities did try to leave the empire, and were treated brutally for it. One might date the treatment of Athenian allies all the way back to the investment of Andros during the Persian War, which was explicitly done, says Herodotus, because the Andrians refused to give money to the coalition. In any case, there is no clear date after which we can speak of the Athenian-led alliance against the Persians as being an empire. The Athenians were always the leaders of the alliance from day one, and were explicitly more powerful than them already in 480. From an early date Athenian willingness to exercise military force over their allies was apparent, and the fact that Athenian allies resolved disputes in Athenian courts speaks clearly to the inferiority of the allies from the start. According to Herodotus the first cleruchs--Athenian settlers on foreign land who maintained their Athenian citizenship--were settled in 505/4 to maintain Athenian power over Chalcis in Euboea. In 475, Thucydides tells us, the Athenians conquered and established a colony (which may have been a cleruchy) at Scyros, whose original (presumably non-Greek) inhabitants, the Dolopes, were expelled. Other cleruchies rapidly appeared in the Aegean. Aegina, for example, was forced in 456 by military power to enter alliance with Athens, and its inhabitants were later replaced by cleruchs, who like all Athenian cleruchs by the latter half of the fifth century were effectively a part-time military garrison. Athenian military power reigned supreme over their allies, and where it was weaker the Athenians attempted to reinforce it.

But as I said, some cities did try to leave, no matter when exactly we want to decide the Athenian-led alliance "became" an empire. Already in 471 Naxos attempted to leave the alliance, after defecting from the Persians during the war. Under Cimon the Athenians reduced the city and planted a cleruchy there. Thucydides says that the city was ἐδουλώθη, "enslaved"--the Naxians likely lost their vote in the league and probably lost political rights in their own city. In 466 the Thasians rebelled, and after three years at siege were likewise reduced. Thasos' walls were torn down, the city was disarmed of its navy, tribute was imposed on it, and its claims to the mainland and mine opposite were transferred to Athens. By the time of the first conflict with Sparta it was clear that acting against the Athenians would be met with military force. During the 440s Miletus was disarmed and forced to pay tribute. When the Milesians called on Athens to help in their territorial dispute with fellow ally Samos, which was still then providing ships to the alliance, the Athenians sent 40 ships to Samos, imposed a garrison, and established a democracy on the island. Likewise Euboea revolted and was put down in 446.

There is only one exception to the destruction of Athenian allies who revolted prior to the Peloponnesian War, at least sort of. Megara revolted from Sparta in 461 and turned to the Athenians, who built a set of Long Walls for the Megarians down to their port at Nisaea, which the Athenians occupied. Although Megara left the Athenian alliance and went back over to the Spartans, Athens continued to garrison her port until 446. But Megara is not particularly normal. She appealed to the Athenians at the outbreak of the first war with Sparta, and was effectively controlled as a conquered outpost--Megara was the stage of much of the war's fighting. She was also a mainland city. Though on the Isthmus, Megara could not be invested as easily by sea as the islands, and could appeal to help from Corinth and Sparta, who could march by land to her aid. Therefore, it's noteworthy that the Athenians held Nicaea for so long, and during the Peloponnesian War proper garrisoned Nicaea until 410, though they were unable during that entire time to take Megara herself (not for lack of trying). Nicaea, as a fortified port, was more like the Athenian possessions in Ionia and the Aegean. Likewise, though landlocked Orchomenus and Acraephnium were briefly tributary after Athenian successes in Boeotia early in the first conflict with Sparta, though the defeat at Coronea ended Athenian rule in Boeotia.

It should also be pointed out that some cities during this time voluntarily chose to join the Athenian Empire. Megara is one example, even though it went back over to the Spartans soon after. Likewise, many cities in Ionia and around the rim of the Aegean voluntarily sided with the Athenians. Recall that war with the Persians continued through the early fifth century, and that many of the cities that joined the empire were Thracian and Ionian cities liberated by the Athenians or who were still under direct threat from the Persians until the 460s. The Athenians, as Thucydides' Alcibiades and Nicias are quick to point out, took and maintained their empire by their willingness to aid their allies. The evidence--largely epigraphic--for dating the changes in Athenian relationships with their allies is difficult to interpret and is frequently debated. But even at a late date, such as when the Athenians began expanding the reach of their alliances into Italy and Sicily, the attraction of a strong ally willing and able to provide military and financial aid in the event of catastrophe appears to have been thought, in many cities, to have been worth the cost of an unequal "alliance."