Why did the Persians keep attacking Greece?

Answer 1

The Greek city-states within the Persian Empire revolted in 499 BCE. Athens and Eretria supported them and in the process burnt down the Persian provincial capital of Sardis. Persia sent and expedition in 490 BCE to take over the cities and instal local tyrants to stop any repeat of this interference. This was repelled at Marathon, and Persia decided that the only way to pacify the mainland cities was to bring them all under control of a Persian governor. Some agreed to this, and Persia sent an invasion force in 480 BCE to take control of the remainder.

Answer 2

The Greek cities of Asia Minor were part of the Persian Empire. They revolted and this brought mainland Greek city-states into the conflict. The Persians decided that the only way to bring peace was to bring all these cities under control. The wars went on for 50 years until the Persians gave up and the Greek cities went back to their usual warfare amongst each other.

Answer 3

The wanted to put an end to Greek interference within their empire, and decided to incorporate the cities within the empire to keep them quiet.