First, the dilemma found in a prophecy about the FINAL FALL of Babylon. Read the two prophecies about Babylon above, Jeremiah on the left, Revelation on the right.

Jeremiah's associate, and 600 years later an Angel in Revelation, are both commanded to throw a stone into the Euphrates river. This action is said to symbolize the same result--that Babylon will be destroyed, never to rise again. The two prophecies were given over 600 years apart. The "dilemma"?

1. If Jeremiah's Babylon (ancient city of Nebuchanezzer) is destroyed never to rise again, how is it that 600 years, long after Babylon fell to the Persians, it receives the same prophecy in Revelation18?

2. Some would say, "Well, the 'system' of Babylon simply moved on to another city, so 600 years later the same prophecy could be repeated in Revelation 18." But still, Babylon would have to "rise again" somewhere for Revelation to repeat that prophecy.

3. Can you legitimately declare Babylon has fallen, never to rise again, if it reemerges in another city? Does Jeremiah's prophecy really mean that the bricks and mortar of ancient Babylon fell, while Revelation's prophecy means that the 'system' of Babylon lives on having simply rotated to another bricks and mortar city, and it, too, is scheduled for a future fall? Why wouldn't Babylon "the system" just continue to move to another bricks and mortar city, ad-infinitum, and make the prophecy totally meaningless?

4. Let's not make a mockery of prophecy and stretch its plain meaning to the irrational. The graphic below shows the confusion of this idea--that Babylon falls twice, each time never to rise again...  

  Jeremiah and  Revelation 18 are "book-end" prophecies...they correlate. Use your marginal verse references in Revelation 18 to see how many (and there are many) phrases and words refer back to Jeremiah 50 & 51 with parallel terms. This fact highlights the truth that both books are talking about the same Babylon in future prophecy. (See--Mark Hitchcock, The Complete Book Of Bible Prophecy, Tyndale House Publishers, Wheaton, IL, 1999, graph p. 100.)

Jeremiah 50-51 is a double-reference prophecy. Nebuchadnezzar's Babylon and End-Time Babylon prophecies are compressed into what is a single prophetic narrative, without distinction to time intervals. This is a common rhetorical devise of the Prophets. BUT NOTE: In ALL references the discussion NEVER changes from Babylon of CHALDEA ! 1

1. The PLACE-- Jeremiah identifies the geo-ethnic identity of Babylon as "Chaldean" (50:1) "Chaldea" word forms are used in Jeremiah 50-51 ten (10) times, all in reference to Babylon. Chaldeans were the people of Biblical Babylon, located in modern-day Iraq, the site of the original ancient city of Babylon. This specific designator, "Chaldea", eliminates any reference to Babylon being any other city or nation outside of Iraq. 

NOTES: Recent DNA (Y chromosome) studies conducted by the National Geographic Magazine on the bones of ancient Babylonians and living people from Babil have shown that the modern peoples carry the same ancient Babylonian genetic material.
McCurry, Steve (2005-02-20). "History: Mesopotamia". National Geographic. http://java.nationalgeographic.com/studentatlas/clickup/mesopotamia.html. 

[ALSO see] url=http://java.nationalgeographic.com/studentatlas/clickup/mesopotamia.html|title=History: Mesopotamia |last=McCurry|first=Steve|publisher=National Geographic|date=2005-02-20|]
[ALSO see] https://enacademic.com/dic.nsf/enwiki/131544
  

2. The TIME--  Jeremiah's Babylon prophecy is set in the days of the Final Salvation of the Jews. (Jer. 50:4-5; 32:40), an event Paul says will happen at the End Time (Rom. 11:25-27).

CONSIDER THIS: "The Babylon mentioned in 1Pe 5:13 was not Rome, as some have thought, but the literal city of Babylon, which was inhabited by many Jews at the time Peter wrote."
Easton's Bible Dictionary, Thomas Nelson Publishing, 1897, "Babylon."