A friend on Facebook raised the question of whether Eternal Security/Perseverance of the Saints is something new to the New Covenant and therefore foreign to the Old. But this seems clearly to contradict the central point of the Book of Hebrews.
The large point of the Book of Hebrews is that the New Covenant is the fulfillment of the Old Covenant by Christ, and is therefore better. And for that reason, the warnings against apostasy are intensified, not lessened. Eternal security is always conditioned on eternal election manifested in true faith accompanied by faith-filled works. The whole point is that there is no difference between the two covenants in this. Those who persevere are saved, those who don’t, aren’t saved, and won’t be saved.
Wherever salvation exists, Perseverance must exist as well, the flip side of it being, as Dr. Sproul put it, God preserving us or persevering with and in us. One might argue that, based off of the failure of the Old Covenant, there was less persevering during the Old. This is a point of those holding to New Covenant Theology, and it is to a degree a fair point. The Old was insufficient in itself, not having the work of Christ, but merely foreshadowing. But in the ebbs and flows of Israel’s relationship with God, we see countless of those in whom salvation was real. This is the focus of Hebrews 12:1-13:1, after all. Abraham, as Paul says, was justified by faith, as were all those after him walking in his faith. Salvation is always at its core the same - to persevere is to be saved.