Decaying is a strong word, as it carries with it the connotation of a long slow collapse. We don't know what would have happened to the Persians if Alexander had not invaded, if he had invaded and took only former Greek colonies in anatolia (many believe this was the extent of Phillip's ambition), or invaded and accepted Darius II's offer of a grant of land and a massive bribe in gold. The Persians may have continued on happily for centuries in any of those possible scenarios.

We do know they were facing some economic hardships. Persia conquered Babylon 200 years before Alexander, and this was their richest territory in terms of producing income for the Persian warrior class. When they took over Babylon they made three main types of land grants to their nobles: horse land, bow land and chariot land. The owners of these grants were expected to provide theking 3 annual levies: flour for the king, a soldier for the king, and taxes for the royal household. All of this is pretty self explanatory. The types of grants are based on the type of soldier demanded, this soldier was required to be a member of the grantholders family. The rest was a tax paid in silver. This worked very well initially, the grants were large and the land of Babylon was exceptionally fertile at this time, producing massive crop yields tat made the Persians very wealthy.

The Persians had a major problem though. They had no rules for primogeniture, in which the first born inherits the family estate in it's entirety. As a result the land grants were divided, and subdivided again and again. Where one man had been expected to come up with enough money to pay the king and equip himself or one of his sons for battle now many much less well off men were expected to come up with the taxes from their share of much smaller farms. The system of taxation which underwrote both the royal court and manned the military was definitely fraying by the time of Alexander's invasion. This created real stresses in the empire, and made it more difficult to raise troops.

You shouldn't read too much into this. The system wasn't working the way it was intended to, but neither was it broken down completely. Darius II was by far the wealthiest man on earth when Alexander invaded. Robin Lane Fox gives a breakdown in his biography of Alexander:

"Alexander’s money expenses already equaled his father’s money income, and a separate debt of 800 talents had accrued for the invasion;the Persian kings received more than 10,000 talents of precious metal as yearly tribute, probably after deduction of the provinces’ expenses, and their palaces housed reserves of metal worth 235,000 talents, some in coin, most in the bar ingots which probably served as currency east of Babylon and north to the river Oxus."

You can see from this that the Persians, while not doing quite as well as their forebears were still very well off.