Just how could Persia lose to Greece?

 

After Darius III realized Alexander had taken the route towards the Tigris, he left Babylon and arrived at central Assyria. Darius III knew the Macedonians would arrive sooner or later, so he looked for a broad battle field for his numerically superior army to form, something that did not happen at Issus. Darius let Alexaner march unhindered, so as to ensure that the Macedonians would not march off to somewhere else. Alexander had done exactly what Darius III wanted him to do. By leaving the fordable stretches of the Euphrates and the Tigris practically unguarded, the Persians had managed to guide the enemy to the battlefield of their choice. Darius was completely in command of the situation and seemed guaranteed of victory. Alexander foolishly fell into Darius's trap.

 

Prior to the battle, the Persians were highly demoralized due to astronomical signs seen in the sky.

Forgive my ignorance, but I think that you are wrong.

Wheter the Persians regained their stuff afterwards or not is fairly irrelevant to the question if they lost. You win and lose wars by reaching or not reaching the political goals you set out to war for. As far as I know Persia did not manage to reach its goals, the Greeks apparently did, and so the Persians lost the war.

The Greeks were never slaves to Persian money. The thing was that the Persians started to wield influence among the Greeks in a more refined and subtile manner than sending massive armies against them, and the with the warlike advantage of the Greeks compared to the wealth of the Persian Empire this proved to be very effective. At no point was any polis, that I am aware of, give up its independence to Persia.