Really? First of all, no one, not even a single Free Grace teacher ever said, that anyone is saved by simply saying (externally) they believe in Christ. Everyone is saved personally (internally) by believing, that is, being persuade that Jesus is the Christ, the guarantor of everlasting life.
Secondly, as the saying goes, "Once saved, always saved" so is, "Once a believer, always a believer", regardless of whether someone says so or not. There are, "unfaithful believers", "forgetful believers", "disobedient children of God", "carnal Christians", those who walk after the flesh, and not by the Spirit. But there is no such thing as a believer, becoming an unbeliever.
One act of faith, one look at the Savior, one drink of the Living Water, one bite of the Bread of Life, one pass through the Door, a sinner becomes a child of God forever. Nothing can ever change that fact. Absolutely nothing "shall be able to separate us from the love of God" (Rom. 8:39), even if a believer becomes faithless, "If we are faithless, He remains faithful; He cannot deny Himself" (2 Tim. 2:13).