Short answer: By the era of the Babylonian conquest, Israel was an internally weak power sandwiched between two warring superpowers. After Nebuchanezzer, the remaining kings of Babylon did not have long reigns. Several were assassinated (hinting to the instability of the country. Then the Persians invaded.
The Land of Israel is sandwiched between Egypt and Mesopotamia (Babylon/Assyria). When either Egypt or the Mesopotamian is strong, Israel fell under the influence of the strong one. When both were weak, that is when Israel, Aram, Philistines, and Tyre flourished and were independent. When both Egypt and the Mesopotamian were strong, they would conquer outward toward each other and their natural meeting place was Israel. Israel was never strong enough to resist either great powers and would have to submit to one of them. Judah was officially conquered by Bablyon in 586 BCE but was under Babylonian hegemony before then.
According to the bible:
Josiah died resisting Egyptian conquest and his son Jeoahaz was an Egyptian puppet.Jehoiakim was also installed by the egyptians but he switched his allegiance to babylon after the egyptians suffered a major defeat. The babylonians then had a setback and Jehoiakim switched sides again, which caused the Babylonians to depose him. Jeconiah, the next king was 8 years old and the babylonians got rid of him. Zedekiah, the last king attempted to court the Egyptians and then the Babylonians decided to end the puppet dynasty and rule Judah directly.