Why did the Gentile woman stop calling Jesus "Son of David" and just say "Lord, help me"?
The Gentile woman stopped saying "Son of David" because that title was a strictly Jewish address tied to Israel's covenant Messiah, and as a Gentile she could not legitimately claim it. Recognizing this, she simply appealed to Him as Lord, saying, "Lord, help me."
Les explains that she came and fell down before Him, saying, "Lord help me." She dropped the term "Thou Son of David" because that was strictly a Jewish address, and as a Gentile she could not use it legitimately, so she learned something and dropped the Son of David bit. Jesus' answer about taking the children's bread and casting it to dogs shows that the children were Israel, the Jews, and the dogs were Gentiles. The reason was covenant promises: He was there to fulfill the covenants made to Abraham, Isaac, and Jacob, and the prophets spoke concerning Israel and their Messiah, not Gentile blessings on Israel's covenant ground. So her changed wording reflects that she no longer approached Him by a Jewish Messianic title but simply as Lord.