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Yes, for sure a backslider can regain his salvation. It doesn’t matter who a person is or what he did, Jesus Christ came into this world to save sinners (1 Timothy 1:15), and we are all sinners (Romans 3:23). No one is outside the reach of God’s saving grace.
Paul spent the first part of his life hating, imprisoning, persecuting and even killing Christians, but when the Lord Jesus appeared to him and changed his life, he became one the Lord’s great disciples. God wants all to be saved (1 Timothy 2:4) and none to perish (2 Peter 3:9; Ezekiel 18:32).
To all those who believe in His name, God gave the right to become His children (John 1:12), and He gives the promise “‘Because he loves me,’ says the LORD, ‘I will rescue him; I will protect him, for he acknowledges my name. He will call upon me, and I will answer him; I will be with him in trouble, I will deliver him and honor him’” (Psalm 91:14–16).
In order for us to experience salvation, we must believe and trust in Him and His sacrifice alone “For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life” (John 3:16; Acts 16:31). And God will cover us with the righteousness of Christ the moment we do this (Romans 3:22).
But the backslider has to turn away from his sin and repent “Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord” (Acts 3:19). Repentance and conversion is the basis of a genuine Christian experience where a man turns away from his old life of sin.
And conversion and change is the work of the Holy Spirit. But the Holy Spirit cannot do His work until a man is willing to let God take hold of his life “Behold, I stand at the door and knock. If anyone hears My voice and opens the door, I will come in to him and dine with him, and he with Me” (Rev. 3:20).