Perseverance
Perseverance is the believer's continuing in faith, endurance, and obedience in Christ. In Calvinism, the "perseverance of the saints" is the claim that every elect person will certainly persevere to the end. Decalvinised distinguishes that claim from eternal security, which rests on God's promise to keep those who are in Christ.
Expanded explanation
The warning passages are addressed to genuine believers and describe real dangers. In Hebrews 6:4–6 and 10:26–29, the danger is not the loss of eternal life but a hardened state in which a believer loses fellowship, fruitfulness, testimony, reward, and inheritance, and comes under God's discipline (Hebrews 12:5–11). Paul describes a believer whose work is burned up: "he will suffer loss, though he himself will be saved, but only as through fire" (1 Corinthians 3:15).
Commands such as "if indeed you continue in the faith" (Colossians 1:23) are therefore meaningful appeals to the believer's will, not merely descriptions of an unavoidable result. Wavering affects the believer's present walk and how he or she is presented to Christ, but it does not undo the new life God has given. Assurance rests on the objective promise of God in Christ rather than on a person's evaluation of his or her own performance.
Context
Perseverance should be distinguished from eternal security, God's preservation of believers, assurance, apostasy, and loss of reward. Calvinist perseverance and once-saved-always-saved are often treated as the same doctrine because they reach a similar conclusion about final salvation, but they differ in their ground, in what they guarantee, and in how they explain someone who falls away.
Non-Calvinists also disagree among themselves; some hold that a believer can abandon faith and be lost. The warning passages are contested and must be read in context. The site's reading that they concern loss of blessing, reward, and inheritance rather than salvation is an interpretive judgment, not an explicit statement of each text.