Q. What did Jesus mean when He said everyone must be "born again"? Can "born-again" people sin and lose out on heaven?
A. John 3:3 is the verse in question. Jesus was indicating that due to our fallen nature, it is necessary to be "born again" of water and the Holy Spirit - a reference to baptism which incorporates a believer into Christ and His Church (cf. Rom 5 and 6; 1 Cor 12).
While baptism removes original sin, it does not remove the human inclination to sin. So, the logical question: "How do I know I am saved?" No absolute assurance is available; one must have recourse to the virtue of hope, which is a firm trust in God's goodness and mercy. Some Fundamentalists hold that someone who is saved "knows" for sure, but St. Paul had some different ideas on the subject. He said the Philippians needed to "work with anxious concern to achieve [their] salvation" (2:12). Paul likewise warned against presumption in this matter: "let anyone who thinks he is standing upright watch out lest he falls" (1 Cor 10:12). Certainly this was also the mind of Christ, who counseled constant vigilance as the best preparation for His coming (e.g., Mt 25).