The first thing that needs to be understood here is why Alexander so easily destroyed Persia. Basically, Persia was a politically rotten and militarily ineffective entity compared to the Macedonian Kingdom. That was the fruit of Philip II's labors, not Alexander's.
If you assume Philip is there, but not Alexander, then Persia still gets smacked around quite a lot. The Greeks had been aware of their relative ability since the Anabasis. The problem was a lack of unity, which is what Philip (and Alexander) gave them.
To assume that no other monarch would come down the road who could fashion a stable enough platform to invade the Persian Empire is ludicrous. Sooner or later, someone would come along, put Greek affairs in order, and use Greek military might to start carving Persia up like a roast goose.
The main difference is that Alexander, being Alexander, took that to extremes. Philip might have settled with carving off the Mediterranean half of the empire, setting up client states, etc, sort of a Macedonian version of the Eastern Empire. Another monarch, like a Pyrrhus of sorts, might have settled for less, say Anatolia and Cyprus or whatever.
So Persia would have survived without Alexander, but as a weakened, destabilized state that would have been expelled from the Mediterranean, in the long term if not the short term. In other words, it would be a lot like what came under the Arascids.