There were many later messianic movements among the Jews. Two of the more important ones were around Sabbatai Zevi in the 17th century (concentrated in the Ottoman Empire, but he had followers in Italy and the Netherlands among other places) and Jacob Frank in the 18th century (concentrated in Eastern Europe). Frank claimed to be the reincarnation of Zevi, which I think gives a sense of the range of Zevi’s influence. Sabbateans were forced to convert to Islam, but remained a separate significant group, particularly in and around Salonica, through the 20th century.

There are more recent messiah claimants, as well. Wikipedia has a handy list. Among recent ones, the Yemenite messiah claimants of the 19th century (the Temani Jews of Yemen were historically very isolated) and the issue of whether the last Rebbe of the Chabad Hasidic dynasty, Menachem Mendel Schneerson, is/was the messiah (tenses get hard when some of the messianists deny he died in 1994) are the two most important. See also Chabad Messianism.

So clearly, Jewish messianism didn’t die out in the 2nd Century if it still exists in the 20th. However, you can also see from an list of messiah claimants that it did die out for a while. Why? First, one of the things the messiah was expected to do was be temporal as well as spiritual ruler. This meant, people at the time often thought, kicking out the Romans. After the Bar Kochba revolt, the Romans scattered the Jews, expelling most from the land of Israel (a previous revolt had already resulted in the destruction of the Temple, the traditional center of Jewish worship).

Some scholars have argued that the resulting Rabbanic Judaism (Judaism of exile, Judaism with text, study, and prayer as the center rather than sacrifice and the Temple) was in some ways *anti-*messianic and that there are several passages in the Talmud that, while recognizing that the messiah will come, urge skepticism at messiah claimants. Some of this skepticism is from Rabbi Akiva, one of the most important Talmudic sages (he founded one of the first yeshivahs, at Javneh) and a former supporter of Bar Kochba. More practically, after defeats that were increasingly decisive, it was probably simply impossible for an radical Jew to reasonably claim to that he was going to defeat the Romans and rebuild Jerusalem. It helps perhaps explain why all Messiah claimants from Bar Kochba to Zevi seemed to have rather small followings, if any. While they could claim to be great spiritual leaders, they had a harder time making claims that were going to be able to end the exile and restore the Temple.