A common caricature of the Reformed doctrine of the perseverance of the saints is that it, supposedly, allows a person to spout some words, and then to live wickedly, assured that he is destined for Heaven. And I grant that the oft-used semi-Arminian version, "once saved-always saved," can be taken exactly that way. That is because the anti-Calvinists don't understand the difference.
As I wrote here, once saved-always saved (hereafter, "OSAS") is the Calvinist doctrine transplanted into an otherwise Pelagian system of theology. It simply doesn't work. In contrast, perseverance holds that God will enable the believer to continue in faith and sanctification. That doesn't mean that the believer can never stumble; rather, it means that he will never ultimately stumble forever.
Consider this verse: "For by a single offering He [i. e., Jesus] has perfected for all time those who are being sanctified" (Hebrews 10:14). Notice the sequence here. By His one offering of Himself on the cross, Jesus has perfected, i. e., legal standing, or justification, those are being sanctified, i. e., progressive sanctification. So the one-time cross work of Jesus saved the elect, so that we have immediate standing as perfect, or holy, and will increasingly experience that holiness in our lives.
That which has already been perfected cannot fail to achieve its purpose!