I think people seriously overestimate the fragility of the Persian Empire at this time. By Guagamela Alexander was far, far from a minor pestilence. If that's all he was, Darius would not have offered him everything west of the Euphrates, now would he? Even by the time of Issus, Alexander's threat was deemed important enough for Darius to raise a large army and march to meet him there. At Guagamela of course, Darius took his time assembling as large an army as he could in one place, with troops from all across the empire and personally lead it-again, not something you do if what is facing you is only a minor pestilence.
And the defections of satraps should not be seen as how close the Persian Empire was to crumbling on its own. You see, when the major army that is defending you in the area is defeated, and you have the choice between remaining loyal to a distant king and hope that the large enemy army in front of you somehow doesn't manage to take your city and satrapy, or decide to cut your losses and cozy up to the guy with the only army in town, the inherent selfishness and self preservation of people kicks in-especially when the conquerer is offering to let you keep your position as it was.
Furthermore, you have to take into consideration the prestige and legitimacy loss that the Great King losing large swathes of territory and two major battles personally, creates. Obviously Darius did not have the support of Ahura Mazda and was not fit to rule if the whole western half of his territory was lost and he lost two major battles himself. Meanwhile, you have this great conqueror who has won this territory and defeated him again and again, and people might start seeing where the wind is blowing and/or thinking maybe this guy is more fit to rule-after all, Alexander was portraying himself essentially as claiming Darius' throne, not destroying the Persian Empire.
To wrap up, there was little sign of imminent doom for the Persian Empire prior to Alexander's invasion. Were they on the decline? Absolutely. Was there shakeups and trouble brewing in the imperial court? Of course, but that was also present between the death of Cyrus and the rise of Darius I and it didn't signal the collapse of the Persian Empire.