Why did the Old Testament canon end with Malachi?

Jewish answer: Our tradition is that from the time of the First Destruction, God's presence was no longer felt as clearly as before (see Deuteronomy 31:17-18). In addition, exile is not conducive to prophecy (Mechilta, parshat Bo). At that time, the living prophets (Haggai, Zechariah and Malachi) realized that prophecy would soon cease; and that the dispersal of the Jewish people, plus the almost continuous tribulations from the First Destruction onwards, made it imperative to seal the canon of the Tanakh (Hebrew Bible). The Sages of the time, including the last prophets, convened a special synod for a couple of decades, which was called the Men of the Great Assembly (Mishna, Avot ch.1). This group, who functioned some 2360 years ago, composed the blessings and the basic prayers of the siddur (prayerbook) and the early portions of the Passover Haggadah, made many of the Rabbinical decrees, and (most importantly) sealed the canon of the Tanakh (Hebrew Bible; O.T.). It was also they who set the twelve Minor Prophets as a single book, and who set the books of the Tanakh in their traditional order (see Talmud, Bava Batra 14b). It was the Men of the Great Assembly whom Esther had to approach when she felt that the Divinely inspired Scroll of Esther should be included in the canon (see Talmud, Megilla 7a).

Since the sealing of the Tanakh, no Jewish sage has ever claimed prophecy.