It is an old and discredited idea that the Achaemenid Persian Empire was in decline when Alexander invaded. In fact, king Artaxerxes III had only recently recovered its richest satrapy, Egypt, after several generations of rebellion. Persia was doing better than it had in a long time. The most obvious evidence for this is the tens of thousands of talents' worth of silver and gold that Alexander looted from Persian imperial palaces.

It would be very misleading to claim that the Persian Empire had recently changed from an aggressive and growing empire to a passive and corrupt leviathan. The expansion of the Persian empire had ceased more than a century before Alexander. It had grown to the point where it was surrounded by natural barriers on all sides, making further campaigns of expansion prohibitively difficult. Both Cyrus and Darius I failed to conquer the northern steppes; Cambyses failed to march through the desert into Ethiopia; Xerxes failed to capture and hold the lands across the Hellespont and the Aegean. On the other hand, no serious enemies remained to challenge the Persians for dominion over their vast territory. The goals of its kings naturally shifted from expansion to consolidation.

While Athenian expansion on the western fringe of the empire actually caused a brief retreat of the Persian sphere of influence, by the early 4th century the cities on the west coast of Asia Minor were once again firmly in Persian hands. The Persians' successful divide-and-rule policy with regard to the Greeks meant that no single state could muster the strength to pose a serious threat to Persian interests, until the rise of Macedon.

Even then, the Persians managed to draw together an army large enough to face its Greco-Macedonian opponents three consecutive times before Achaemenid power was decisively broken. Far from an ineffective reponse, the Persian defence against Alexander was a staggering display of imperial power. Given that tens of thousands of the Persian infantry were in fact Greek mercenaries, the cost of raising and maintaining this army must have been incredible, yet Persian coffers could easily carry the burden - while simultaneously maintaining a fleet vastly larger than its Macedonian counterpart.

It is true that the Persians faced rebellions in its semi-autonomous satrapies throughout the latter years of its history, but these were usually effectively dealt with by Imperial armed force. As noted above, Egypt was retaken less than a decade before Alexander invaded. All previous rebellions had been quashed; no part of the Persian Empire ever successfully broke away.

Really, the only reason to assume the Persian Empire was in crisis is the fact that it suffered dynastic troubles in its final years, with two successive kings being allegedly assassinated before Darius III restored order. However, it's worth noting that it was another dynastic crisis nearly two centuries earlier that led to the accession of Darius I, one of the most capable and successful of the Achaemenid kings. We might have a very different view of the period if Alexander had invaded a decade later.

The standard work on Persian history is Pierre Briant's From Cyrus to Alexander: A History of the Persian Empire.