I’ve always been told you can forfeit your salvation. It sounds like you are saying this is impossible when you give your life to Christ. Can’t people backslide?
You have touched upon a very important issue. Over the last fifteen years, emphasis on the ability to save has been shifted from God to Man. As a result, the permanency of salvation has been called into question, because this approach to salvation emphasizes that believing certain truths can save a person and then that same person can subsequently lose his/her salvation by disbelieving those same truths. However, the Bible clearly teaches that salvation is based solely on God’s Spirit coming into the spirit of a human being; and in so doing, causing that person to become a new creation, a new person. A person’s experience of regeneration by the Holy Spirit is an act of God, not of man.
Biblically, the salvation process begins with God the Father. Jesus said, in John 6:44, “No one is able to come to me, unless the Father who has sent me should draw him; and I will raise him up in the last day.” In John 3:3 , Jesus says, “Unless anyone should be born from above, he is not able to see the kingdom of God.” Consequently, if the Father does not draw a person to Christ, that person cannot be saved. It is only after the Father has drawn someone to Christ, that the Spirit of Christ enters into the spirit of that person and spiritual birth takes place.
These same truths are taught by the Apostles. Paul, in Titus 3:5  wrote, “Not out of works in righteousness which we did, but according to His mercy He saved us, through washing of regeneration, and renewing of the Holy Spirit.” Peter said, in 1 Peter 1:3 , “Blessed is the God and Father of our Lord Jesus Christ, the One who according to his great mercy has regenerated us again into a living hope through the resurrection of Jesus Christ from the dead.”
In the early Church, the requirement for salvation was the presence of God’s Spirit dwelling within a person. Paul instructed, in Romans 8:9 , “Now if anyone does not have the Spirit of Christ, this one is not of Him.” In Romans 8:14 , he wrote, “For as many as are being led by the Spirit of God, these are the sons of God.” And again, in Romans 8:16 , he instructs that “The Spirit itself bears witness with our spirit, that we are children of God.” Also, in 2 Corinthians 13:5 , Paul challenged the church at Corinth: “Examine yourselves, if you are in the faith; prove your own selves, or do you not know your own selves, that Jesus Christ is in you, except you are reprobates?”
John, writing in 1 John 3:24  supported this same understanding: “And in this we know that He abides in us, from the Spirit whom He has given to us.” He repeats this same truth, although worded somewhat differently, in 1 John 4:13 , “In this we know that we dwell in Him, and He in us, because He has given to us of His Spirit.”
From the preceding scriptures, we see that salvation happens only when God’s Spirit enters and remains in a person’s spirit, thereby causing spiritual birth. Nothing in the Bible teaches that salvation is accomplished by the repetition of the Sinner’s Prayer or through the performance of any other kind of human formula.
In addition to teaching that God is the sole source of salvation, the Bible also teaches that every saved person is kept by the power of God. Peter writes, in 1 Peter 1:5 , that believers are, “The ones who are being kept in the power of God through faith for salvation ready to be revealed in the last time.” Paul writes on the same subject, in Galatians 5:17 , “For the flesh lusts against the Spirit, and the Spirit against the flesh; and these are opposing to one another; in order that you should not do what you want.” These scriptures show that believers cannot be taken away from Christ by the flesh, because the Spirit of God is dwelling within to prevent that from happening.
Jesus Himself said, as recorded in John 6:37 , “All that the Father gives to me will come to me; and the one coming to me I will never cast out.” He goes on to say, in John 6:39 , “And this is the will of the Father who has sent me, in order that of all which he has given to me I should lose nothing, but should raise it up in the last day.” Also, in His prayer to the Father, as recorded in John 17:11-12 , Jesus said, “And now I am no more in the world, but these are in the world, and I am coming to you. Holy Father, keep through your own name those whom you have given to me, in order that they may be one, as we are. When I was with them in the world, I was keeping them in your name; the ones who you have given to me I kept, and none of them perished, except the son of perdition; in order that the Scripture might be fulfilled.”
I emphasize the permanency of salvation because the Bible teaches that God is the One who saves and He does so from out of His mercy. According to Paul, in Ephesians 2:8 , grace, faith, and salvation are gifted from God.John says, in John 1:13 , believers “were born, not from blood, nor from the will of the flesh, nor from the will of man, but from God.” Therefore, according to Scripture, a human being cannot save him/herself.
We also know from Scripture that no one can keep himself saved. John teaches, in 1 John 5:18  (as recorded in the oldest Greek manuscripts), “We know that everyone who has been born from God does not practice sin; but the one who has been born from God, God is keeping him and the evil one does not touch him.” John also states in John 10:27-29 , “My sheep hear my voice and I know them; and they follow me. 28) And I give to them eternal life; and they will never perish forever and not anyone will seize them from out of my hand. 29) My Father who has given them to me is greater than all, and no one is able to seize them from out of the hand of my Father.” Jude states in his doxology in verse 24, “But to the One being able to keep you without stumbling and to set you before His glory blameless in exultation.” Paul in his writings emphasized the keeping power of God’s Spirit in Ephesians 1:13-14 : “In whom also after having heard the Word of truth, the gospel of your salvation, in whom also, after having believed, you were sealed with the Holy Spirit of promise, 14) who is the guarantee of our inheritance, for redemption of the possession, for the praise of His glory.” He states again in Ephesians 4:30 , “And do not grieve the Holy Spirit of God in whom you were sealed for the day of redemption.” Probably one of the most powerful Scriptures of God’s keeping power is Romans 8:38-39 : “For I am persuaded that neither death, nor life, nor angels, nor rulers, nor powers, nor any thing which has come, nor things coming, 39) nor height, nor depth, nor any other created thing will be able to separate us from the love of God, which is in Christ Jesus our Lord.” The only way a person can be saved is by a spiritual birth from God; and the only way a person can keep his salvation is through the keeping power of God.
Many scriptures were written to show believers that some among them, who professed to be Christians, were actually not saved. John wrote I John so those who were saved would know that they have eternal life (1 John 5:13 ). In this letter, he listed many evidences, so that salvation could be proven among genuine believers. In 1 John 2:18-19 , he writes, “Little children, it is the last hour; and according as you heard that antichrist is coming, even now many antichrists have come; from this we know that it is the last hour. They went out from us, but they were not of us; for if they were of us, they would have continued with us; but they went out, in order that they might be made manifest that they were not all of us.” John is stating that those who are of the antichrist came out from the Christian fellowship. He teaches that the reason they chased after false doctrine and a false spirit, not staying with the fellowship of believers, is because they were never truly believers.
Sadly, the same is true today. There are many in our churches professing to be Christians, but who have no desire to hear or obey the truth of God’s Word. Indeed, many so-called church leaders are not even teaching the Word of God from their pulpits, because they don’t want to lose the numbers of people attending their services. But the truth from God’s Word still differentiates those who are truly saved from those who are just talking and acting like Christians, being devoid of the indwelling Spirit of Christ.
This is what the Bible teaches about salvation. The change in emphasis from salvation by God to salvation by man is part of the apostasy of the last days. The truth is, many today are told that they are saved because of some followed formula; but Jesus said believers would be known by their fruits, not by their human works (Matthew 7:16 ). He also said, in Matthew 7:21-23 , “Not everyone saying to me, ‘Lord, Lord’ will enter into the kingdom of heaven; but the one doing the will of my Father who is in heaven. Many will say to me in that day, ‘Lord, Lord, did we not prophesy in your name? And in your name did we not cast out demons? And in your name did many works of power?’ And then I will confess to them, ‘I never knew you; depart from me, the ones working lawlessness.’”
As for your second question, backsliding is not found in the New Testament and is never applied to the believer in Christ. It is strictly an Old Testament term describing the Children of Israel.