There are a number of reasons, from simple luck (Salamis and Plataea, the two decisive battles, were by no means preordained Greek victories) to other historical events, such as a major series of rebellions at the beginning of Xerxes' reign, to simple logistical distance. One factor that is often ignored, however, is that the Greeks were not the plucky, free spirited underdogs they are often portrayed as, including by themselves. Athens, or at least Athens' great families, had already acquired a significant Aegean quasi-colonial empire before Darius' invasion, and Greek city states could project political will into the western and eastern Mediterranean. The natures of the political economies involved means that while Persia's available resources dwarfed any Greek city state's, the Greek cities were much better at mobilizing their resources.

I can go into detail about this when I have a computer, but generally speaking the Greeks tended to downplay their material and manpower capabilites.