Salvation by grace is different from other standards of right-standing with God across the ages.
From the beginning of redemption up to the Cross God saved those who worshipped Him, called on His name, walked with Him, believed in Him convinced that He will do what He said He will do.
Under the New Covenant salvation is by grace alone.
For a born again Christian to become an eternal son of God he or she must be transformed into Christ-likeness.
A born again Christian has eternal life. Eternal life is resident in the Lord Jesus Christ and given to those who believe in Him.
However, a born again Christian can cease to be born again at the point of physical death or the rapture of dead and living Christians whichever occurs first. This can happen for failure to attain an inseparable union between the created Inward Personality comprising spirit and soul and the uncreated but implanted Hypostatic Chip, a son of God, which is the image of God in redeemed mankind.