As Sol Hachuel boldly declared, "I was born a Jew, and I shall die a Jew."
I suppose you are referring to behavior (i.e., Jews who aren't behaving like Jews). In that case, any number of things (secularism, spiritual apathy, lack of Jewish education, threats of bodily harm, etc.) can provide an avenue for a Jew to cease behaving like a Jew. Faith in Messiah Yeshua is merely one of many possible causes.
I condemn the prevailing error within Christianity that encourages or requires Jews to abandon their covenantal Torah obligations when they become believers in Jesus. Such encouragement or requirement is entirely without basis in Scripture! The Prophets condemned such behavior when it occurred in their day. Messiah, Himself pointed out this error in His message to believers in Pergamum (Revelation 2:14), where some held the "teaching of Balaam, who kept teaching Balak to put a stumbling block before the sons of Israel, to eat things sacrificed to idols and to commit immorality".
If you are referring to intermarriage, then, once again, faith in Messiah is far from the sole source of that threat to Jewish identity. My position and that of the Psalm 119 Foundation (based, I believe, upon the teaching of Scripture) is that any person who would desire to marry a Jew should also become Jewish through conversion. Again, Scripture provides the example of Boaz and Ruth, where the Torah would have forbidden Boaz to marry Ruth, a Moabite woman. Since Scripture offers no condemnation to Boaz for his apparent intermarriage and instead esteems both him and Ruth as the forebears of King David, it appears Ruth converted to Judaism (as indicated by her declaration to Naomi: "your people will be my people and your G-d will be my G-d").
Perhaps a shorter answer to this question would be: "it depends".
It depends upon the Jewish individual. For example, we know a sixth-generation Jewish believer in Messiah who remains Torah observant (along with his Gentile-convert-to-Judaism wife and their son). Far too often, however, it is usually zero generations: the Jew who becomes a believer in Jesus often abandons their Jewish identity and Torah observance immediately. This is tremendously sad and unfortunate.
One of my goals through the Psalm 119 Foundation is to encourage Torah observance among all believers in the Messiah Yeshua—observance appropriate to the individual's position within the Congregation of Israel, whether that person is a Jew or Gentile. I pray that I am contributing somehow to tikkun olam and restoring G-d's perfect Law to the world.
