The appearances of the Angel of the Lord ceased after the incarnation of Christ Jesus; when God the Son became a man.
One day, the Angel of the Lord appeared to Samson's parents announcing that they would have a child (Samson.) At that time, Samson's father asked the Angel of the Lord what His name was so that he and his wife could honor Him. In reply, the Angel of the Lord said, "Why do you ask My name, seeing it is wonderful?"1 Many centuries later, the prophet Isaiah prophesied about God the Son becoming a man. This is what He said: "For unto us a Child is born, unto us a Son is given; and the government will be upon His shoulder. And His name will be called Wonderful, Counselor, Mighty God, Everlasting Father, Prince of Peace.”2
The Bible, also, says that the Angel of God, accompanied the Israelites as they left Egypt; this happened long before the birth of Christ Jesus, in Bethlehem, Judea, a little over 2000 years ago. The Angel of God is identified, by the Bible, as a pre-Bethlehem appearance of Christ Jesus; the spiritual Rock that accompanied the Israelites.3
1 (Judges 13:18)
2 (Isaiah 9:6, New King James Version of the Bible)
3 (Exodus 14:19; 1 Corinthians 10:1-4)