Is the term, "the great falling away" directly from the Bible, capitalized when used in a sentence to emphasize its importance? Also, the term "last days" is in question.
Some terms are always capitalized, like Holy Ghost.
The "great falling away" (=apostasy/rebellion - 2 Thessalonians 2:3) is less talked about than the Flood or the Second Coming, but if you interpret it as a single and major event, you could argue for its capitalization. Otherwise, I would caution against it (but context matters).