The question comes up once in a while. Why do some people believe that the Messiah is eternal? Some base their answers only on Biblical texts such as the following found in the Bible: Both the Old Testament and the New Testament confirm the Messiah's eternal nature.
By examining Biblical texts we can see evidence as to not only the eternal nature of the Messiah but Messiah's divinity as well.
Other articles that help to support this position include:
Outside of the Biblical texts that have been canonized there are more writings to show that other sources besides the Bible itself accept that the Messiah is of an eternal nature:
(Babylonian Talmud, Pes. 54a; B. Ned. 39a)
In the apocryphal First Book of Enoch, which was originally written in Hebrew or Aramaic about 150 B.C.E.
The Messiah has been a part of Jewish Messianic eschatology since well before the birth of Jesus 2000 years ago.
Mashiach and the Messianic age were preconceived from the very beginning, for which the world was created.(1) Mashiach, therefore, is one of the things that precede the creation.(2)
Some rabbis insisted that the Messiah's name was identical with, or similar to, the name of the sage whose students they were (R. Shelah - Shiloh; R. Hanina - Hanina; R. Yannai - Yinnon).
1). The Principle of Mashiach and the Messianic Era in Jewish Law and Tradition by Jacob Immanuel Schochet p. 34. In reference to Sanhedrin 98b; Pesikta Rabaty 34:6 (ed. Friedmann, ch33). See also Bereshit Rabba 2:4 and cf. R. Bachaya on Genesis 1:2 and Netzach Yisrael, ch 43.
2). The Principle of Mashiach and the Messianic Era in Jewish Law and Tradition by Jacob Immanuel Schochet p. 34 In reference to Pesachim 54a; Pirkei deR. Eliezer ch.3 (see there Bi'ur Haradal note 14); Bereishit Rabba 1:4 (and see there Minchat Yehudah). Cf. Yeshu'ot Meshicho, Iyun Hasheni: ch.3.
See also: Midrash: Breisheet I: Creation http://www.bibletopics.com/biblestudy/70a.htm
Source: "The Messiah Texts", by Raphael Patai (Avon Books, 1979)