Why did some books mentioned in the Bible perish and not make it into the canon? Were they not inspired?
Some books the Bible mentions were not inspired but are simply used as historical sources. This is the case when Paul quotes books by the pagan writers Aratus, Menander, and Epimenides (Acts 17:28, 1 Cor 15:33, and Ti 1:12, respectively) or when the Old Testament refers us to the book of the Annals of the Kings of Media and Persia (Est 10:2).
The same is likely true of the book of the Annals of the Kings of Israel (1 Kgs 14:19) and the book of the Annals of the Kings of Judah (1 Kgs 14:29), which may simply have been court records or secular histories of the periods they discussed. The same goes for the book of the Kings of Judah and Israel (2 Chr 16:11), and the Memoirs of Nehemiah (2 Mc 2:13).
Other books contained genuine revelation, though the book as a whole was not inspired. This is the case with the book of Enoch, which is quoted in Jude 14, and possibly a book known as the Assumption of Moses, which appears to be quoted in Jude 9. A work of unclear status is the book of Jashar, which is twice quoted in the Old Testament (Jo 10:12-13, 2 Sm 1:18-27) and seems to be a book of songs concerning the history of Israel.
Among uninspired books mentioned in the Old Testament are the Records of Samuel the Seer, the Records of Nathan the Prophet, and the Records of Gad the Seer (1 Chr 29:29), the Prophecy of Ahijah the Shilonite, the visions of Iddo the Seer concerning Jeroboam son of Nebat (2 Chr 9:29), the Records of Shemaiah the Prophet and of Iddo the Seer (2 Chr 12:15), the Annotations of the Prophet Iddo (2 Chr 13:22; the references to works of Iddo may be different ways of referring to the same book).
In the New Testament, there are references to a third letter from Paul to the Corinthians (1 Cor 5:9) and of a letter of his to the Laodiceans (Col 4:16; though many have thought this letter to the Laodiceans is the same as the letter to the Ephesians). Such books may have been inspired, but for some reason God chose not to have them passed down and included in the canon.