This promise has been fulfilled. After Babylon was taken by the Parthians in about 144 BC, the city had become completely powerless. “By the time of Christ, only a few astronomers and mathematicians continued to live in the ancient, sparsely populated city. After they left, Babylon remained a deserted tell (mound), which sand and brush gradually covered until it became a hill used only by wild animals, and as grazing land for nomadic flocks” (Isaiah: Prophet, Seer, and Poet, by Victor L. Ludlow, p. 185). Even today, the ancient city of Babylon is barren, completely uninhabited, and only of interest for its archeological value. The site of the city is in modern day Iraq, not far from Baghdad.
The prophet, Jeremiah, also prophesied that Babylon would eventually be completely desolate, never to be inhabited again. This is what the Lord had done to Sodom and Gomorrah:
’Because of the wrath of the Lord it shall not be inhabited, but it shall be wholly desolate: every one that goeth by Babylon shall be astonished, and hiss at all her plagues.
Therefore the wild beasts of the desert with the wild beasts of the islands shall dwell there, and the owls shall dwell therein: and it shall be no more inhabited for ever; neither shall it be dwelt in from generation to generation.
As God overthrew Sodom and Gomorrah and the neighbour cities thereof, saith the Lord; so shall no man abide there, neither shall any son of man dwell therein.’ (Jer 50:13,39-40)
LeGrand Richards
“[Babylon] was the greatest city in all the world….Yet Isaiah announced that that city would be destroyed; he said that it would never be rebuilt, that it would never be inhabited from generation to generation, that it would become the abode of reptiles and wild animals and that the Arabs would no more pitch their tents there. That was a declaration that the greatest city in the world would not only be destroyed, but it would also never be rebuilt.” (Conference Report, Apr. 1954, p. 54 as taken from Latter-day Commentary on the Book of Mormon compiled by K. Douglas Bassett, pp. 147-7)