The Epistle to the Hebrews provides overwhelming exegetical support against the pernicious doctrine of eternal security (AKA perseverance of the Saints). I have discusses this topic before on this blog, including:
Another key text from this epistle (which is my favourite book in the NT, btw) is that of Heb 3:1, 6 which reads:
Therefore, holy brethren, partakers of a heavenly calling, consider Jesus, the Apostle and High Priest of our confession . . . but Christ was faithful as a Son over His house--whose house we are, if we hold fast our confidence and the boast of our hope firm until the end. (NASB)
Commenting on this text, one critic of the Protestant doctrine of Sola Fide wrote:
Here, the address is to “holy brothers,” not people of quasi-Christian sentiment. The word “if” introduces a Greek fifth class conditional sentence in a present general supposition. The apodosis contains the present indicative (“whose house we are”) and the protasis contains εαν with the subjunctive verb κατασχωμεν (“if...we hold on to”). Of the six classes of Greek conditionals, this is one of the strongest. In both classical and koine Greek, it specifies, without any contingencies, that the apodosis cannot be or come true unless the protasis is satisfied. (See Smyth, Herbert W. Greek Grammar (Cambridge, MA: Harvard University Press, 1920, 1980), p. 528). (Robert A. Sungenis, Not by Faith Alone: The Biblical Evidence for the Catholic Doctrine of Justification [2d ed.; Catholic Apologetics International Publishing, Inc., 2009 ], 267-68, n. 320)