Perhaps someone has a more authoritative answer, but I'll try to explain as best I understand it: The KJV (as well as most of its predecessors, eg: Tyndale, Coverdale, Geneva Bible, etc) were based off of manuscripts that were available at the time. We hadn't found the dead sea scrolls amongst other ancient manuscripts that most modern translations also consider when selecting their translations.

To quote one website's explanation of the KJV's translation sources:

"Five of the oldest manuscripts were not used. The Alexandrian and Vatican texts were known to exist, but were not available to the translators. Three other manuscripts (Sinaiticus, Beatty papyri, and Bodmer papyri) had not yet been discovered... In the late 1800’s and 1900’s a number of Egyptian papyrus documents were discovered in ancient garbage dumps. Many of the papyrus documents helped explain the meaning of some new testament words. These discoveries have made some major contributions to our ability to accurately translate the Bible."

So in essence, we have older documents to consult

Another website suggests [More authoritative sources welcome here] the source of the less popular "did not cease to prophesy" translation is the Targumim ("commentaries the rabbis wrote on the Old Testament scriptures long after the time of Jesus") but that even the Greek old testament documents which would have been available at the time indicate the opposite ("did cease to prophesy").

One other potential spot for confusion here, is the phrase ולא יספו (transliterated: lo yasaf), which is what becomes translated as did (or did not) cease. Yasaf usually means to add, increase, or do again/repeat. Lo typically means no or not, but also occasionally without or before. I'm no expert at Hebrew, so I can't speak authoritatively here about which combinations are reasonable or not, but I would imagine that if additional ancient documents surfaced using this combination of words, since the time of the first translation, context in the additional documents could provide additional examples to make one translation of the combined phrase more certain than another in later translations.

It's also worth noting that with a pre-christ worldview, we would not expect the elders to continue to prophesy indefinitely, we would expect that, consistent with other texts in the old testament, the spirit came and went as he pleased, such that the elders may have continued to prophesy without ceasing for a short period of time (like perhaps until the end of the day), but it would be strange to suggest they retained the spirit permanently to prophesy on an ongoing basis, which the KJV translation might erroneously lead one to believe.

Perhaps someone has a more authoritative answer, but I'll try to explain as best I understand it: The KJV (as well as most of its predecessors, eg: Tyndale, Coverdale, Geneva Bible, etc) were based off of manuscripts that were available at the time. We hadn't found the dead sea scrolls amongst other ancient manuscripts that most modern translations also consider when selecting their translations.

To quote one website's explanation of the KJV's translation sources:

"Five of the oldest manuscripts were not used. The Alexandrian and Vatican texts were known to exist, but were not available to the translators. Three other manuscripts (Sinaiticus, Beatty papyri, and Bodmer papyri) had not yet been discovered... In the late 1800’s and 1900’s a number of Egyptian papyrus documents were discovered in ancient garbage dumps. Many of the papyrus documents helped explain the meaning of some new testament words. These discoveries have made some major contributions to our ability to accurately translate the Bible."

So in essence, we have older documents to consult

Another website suggests [More authoritative sources welcome here] the source of the less popular "did not cease to prophesy" translation is the Targumim ("commentaries the rabbis wrote on the Old Testament scriptures long after the time of Jesus") but that even the Greek old testament documents which would have been available at the time indicate the opposite ("did cease to prophesy").

One other potential spot for confusion here, is the phrase ולא יספו (transliterated: lo yasafu), which is what becomes translated as did (or did not) cease. Yasaf usually means to add, increase, or do again/repeat. Lo typically means no or not, but also occasionally without or before. I'm no expert at Hebrew, so I can't speak authoritatively here about which combinations are reasonable or not, but I would imagine that if additional ancient documents surfaced using this combination of words, since the time of the first translation, context in the additional documents could provide additional examples to make one translation of the combined phrase more certain than another in later translations.

It's also worth noting that with a pre-christ worldview, we would not expect the elders to continue to prophesy indefinitely, we would expect that, consistent with other texts in the old testament, the spirit came and went as he pleased, such that the elders may have continued to prophesy without ceasing for a short period of time (like perhaps until the end of the day), but it would be strange to suggest they retained the spirit permanently to prophesy on an ongoing basis, which the KJV translation might erroneously lead one to believe.