There is always more to say, but I have written about this before for another question. In that answer I focus on the Persian period, but also explain the slow decline of Babylon in the Seleukid and subsequent periods of the city's history. The condensed version is essentially that it remained a prominent capital city within the Persian Empire until the reign of Xerxes, at which point it declined slightly, only to see a brief renaissance under Alexander the Great and then a drastic decline under his successors.

I'd also like to comment on the Biblical basis for your question. I don't know anything in particular about John Walvoord or his personal religious leanings, and I certainly don't want to to dismiss anyone's religious beliefs out of hand. That said, you posted this to r/AskHistorians and I feel like I should give the historians' perspective on the topic. Judging from the language of the quote, the prophecy (if its even the right word for the stories at the beginning of the book) in question here is the book of Daniel. Secular scholars generally consider Daniel to be a very late addition to the canon, written many centuries after the events it describes. The stories at the beginning of the book, like the angel in the furnace, the writing on the wall, and Daniel in the lions' den are thought to be folk stories that developed in the centuries after the Babylonian Exile.

Critically for this question, that explains a lot of the historical inconsistencies in the book. Daniel describes how King Nebuchadenzzar of Babylon exiled the Jews, how he was succeeded by King Belshazzar, how Belshazzar was defeated by Darius the Mede, and how these kings all punished the Jews for their faith at some point.

Nebuchadnezzar did deport the Judeans to Babylon, but he was not succeeded by Belshazzar. Belshazzar was the son of Nabonidus, and never actually succeeded his father to the throne. There were three kings between Nebuchadnezzar and Nabonidus, only one of whom was a son of Nebuchadnezzar (Amel-Marduk). Nabonidus was king, and Belshazzar was crown prince, when Babylon was conquered. Babylonia fell to Cyrus the Great of Persia, rather than Darius the Mede. The difference between Mede and Persian can probably be forgiven because Greek literature only really drew a distinction when it had to discuss the Medes and Persians in opposition to one another, but it's an interesting distinction for the author of Daniel to make. Darius is a name from Persian history, but the name of the 4th, 9th, and 13th kings of the Persian Empire, rather than the first.

It's interesting to note that Darius the Great (the 4th Great King of Persia) did have to conquer Babylon. In fact, he did it twice, both times defeating a king who took the name Nebuchadnezzar. However, these were battles against rebels a generation after Babylon had been subjugate and the Jewish exile was legally ended.

Then we come to the issue of religious persecution. Contrary to the picture painted by the Hebrew Bible (especially later texts like Daniel and Esther), there really wasn't much religious persecution in the ancient Middle East. There were thousands of gods, each with hundreds of thousands of devotees and traditions associated with them. No ancient Near Eastern kingdom ever tried to enforce a particular religion or system of worship on conquered peoples because it just wasn't practical or enforceable. There also wasn't much of a tradition of god-kingship in the region at the time, so none of the stories about kings demanding that they be worshiped and Jews refusing because they would only worship god make any sense in historical context. The Jews may have faced political persecution since Israel and Judea occupied some pretty valuable land between Egypt, Syria, and the Mediterranean. They may also have faced some ethnic persecution because they were a small group with unique traditions, but overall which god or gods they worshiped probably wasn't a huge factor in Assyrian and Babylonian aggression.

The idea of religious persecution makes even less sense under the character of Darius the Mede (who threw Daniel to the lions). He seems to be some kind of amalgam of the various Darius names in Persian history and Cyrus the Great, but that contradicts the rest of the Hebrew Bible. Cyrus the Great is famously the only non-Jew to be called a Messiah because it was his conquest of Babylon that ended the exile in Babylon. Darius the Great is credited by Ezra as the king who provided funds and supplies to rebuild the Temple in Jerusalem. They're both about as far from religious persecutors as you can get.

All of this makes a bit more sense when you realize that the form of Daniel we see in the Biblical canon was probably written down in the 2nd century BCE. This was a time of increased persecution, when the Seleukid king, Antiochus IV, was actively persecuting the Jews for their religious beliefs and trying to force them to acknowledge him as a god-king.

The primary evidence for this is language, style, and subject matter. There is no evidence for the book of Daniel in Hebrew, but many manuscripts in Greek and the style consistent with Hellenistic Greek rather than Second Temple Hebrew. The latter half of the book is an Apocalypse (as in the genre of biblical literature, not necessarily the event) and attributes its authorship to a minor figure mentioned briefly in earlier books of the Hebrew bible. Both of these traits were extremely common in Hellenistic-era Jewish literature. Finally, the prophetic second half of the book discusses the reign of the Antiochus IV, in very accurate detail, but only up to his destruction of the Temple in Jerusalem. After that event, the prophecy keeps going, but is entirely incorrect. The consensus is that the text must have been composed and become popular in the middle of Antiochus IV's reign, and thus the end of the prophecy was a failed attempt to predict the future, while the first part of the prophecy was recounting recent events.