As found in writings of Rabbi Aryeh Kaplan, one of the arguments used by Anti missionaries to explain why we don't believe Jesus was the messiah, was his epic failure to bring world peace and universal belief in God. To which the missionaries point to their beleif of the second coming, when messiah comes back to finish the job. This idea is dismissed as a sorry excuse for his failure, as the Jewish. prophets only mentioned a single arrival of the Moshiach. If we take for granted that there will be a twofold arrival of Moshiach, namely Moshiach ben Yosef and afterwards the Moshiach ben Dovid, does this ruin the argument? Does the fact that they are presumably two different people make a difference?
First, there is the question of "taking for granted" that there will be a MB"Y -- on this...
Quite significantly, R. Saadiah Gaon (one of the few to elaborate on the role of Mashiach ben Yossef) notes that this sequence is not definite but contingent! Mashiach ben Yossef will not have to appear before Mashiach ben David, nor will the activities attributed to him or his death have to occur. All depends on the spiritual condition of the Jewish people at the time the redemption is to take place:
The essential function of Mashiach ben Yossef is to prepare Israel for the final redemption, to put them into the proper condition in order to clear the way for Mashiach ben David to come. Of that ultimate redemption it is said, that if Israel repent (return to G‑d) they shall be redeemed immediately (even before the predetermined date for Mashiach's coming). If they will not repent and thus become dependent on the final date, "the Holy One, blessed be He, will set up a ruler over them, whose decrees shall be as cruel as Haman's, thus causing Israel to repent, and thereby bringing them back to the right path."14 In other words, if Israel shall return to G‑d on their own and make themselves worthy of the redemption, there is no need for the trials and tribulations associated with the above account of events related to Mashiach ben Yossef. Mashiach ben David will come directly and redeem us.
from http://www.chabad.org/library/moshiach/article_cdo/aid/101747/jewish/Appendix-II.htm which footnotes to Emunot Vede'ot VIII:6; see there at length. Cf. Or Hachayim on Numbers 24:17.
But if one sees that the MB"Y will come, two factors are required -- 1, that he dies in a war as a military leader and 2, that the events which follow to usher in the MB"D happen soon thereafter.
The immediate results of this war11 will be disastrous: Mashiach ben Yossef will be killed. This is described in the prophecy of Zechariah, who says of this tragedy that "they shall mourn him as one mourns for an only child." (Zechariah 12:10).12 His death will be followed by a period of great calamities. These new tribulations shall be the final test for Israel, and shortly thereafter Mashiach ben David shall come, avenge his death, resurrect him, and inaugurate the Messianic era of everlasting peace and bliss.13
- Targum Yehonathan on Exodus 40:11, and on Zechariah 12:10 (manuscript-version in ed. A. Sperber); Agadat Mashiach; Pirkei Heichalot Rabaty (in version cited by Ramban, Sefer Hage'ulah, sha'ar IV; ed. Chavel, p. 291); and Rashi on Sukah 52a; identify the battle of Mashiach ben Yossef with the war of Gog and Magog.
- Sukah 52a, and parallel passages.
- Pirkei Heichalot Rabaty, ch. 39 (cited in Sefer Hage'ulah, sha'ar IV); Sefer Zerubavel; Agadat Mashiach (cited in Lekach Tov, ibid.). See R. Saadiah Gaon, Emunot Vede'ot VIII:ch. 5, adding Scriptural "prooftexts" or allusions for all details; and the lengthy responsum of R. Hai Gaon on the redemption, published in Otzar Hageonim on Sukah 52a, and in Midreshei Ge'ulah, ed. Y. Ibn Shemuel, p. 135ff. Cf. Rashi and Ibn Ezra on Zechariah 12:10; Ibn Ezra and Redak on Zechariah 13:7.
The traditional concept of Moshiach ben Ephraim (also known as Moshiach ben Yosef) does not undermine the criticism that Nazarene has not fulfilled significant Messianic prophecies.
Even if we could concede hypothetically that the tradition of Moshiach ben Ephraim gave some legitimacy to the belief that the Nazarene would "continue" or "complete" his purported Messianic mission even after he died, such a concession would have rapidly become irrelevant when the "fulfillment" of the messianic mission proper wasn't subsequently realized. The events associated with Moshiach ben Ephraim take place, at any rate, at the time of the redemption so the delay of the Messianic redemption until long after the life of those involved in its alleged commencement is inconsistent with the picture we see in the Scripture or in tradition. In other words, the real or perceived similarities between Christian belief about the Nazarene and these aspects of the redemption doesn't diminish the difficulty posed by the unfulfilled prophecies.
Furthermore the fact that Moshiach ben Ephraim is a distinct individual from the Moshiach is significant (see Zechariah 2:4 and Obadiah 1:21, traditional verses from which the notion of MBE is sourced). It is difficult to argue that the Messiah's mission will be interrupted for an extended period based on the difficulties of an entirely other player in the events.
The notion of Moshiach ben Yosef not withstanding, the prophecies remain unfulfilled and an assertion that they will be fulfilled later isn't a fulfillment....