The following is from Donald C. Stamps, Life in the Spirit Study Bible, pp. 1962-63:
The Greek words for apostasy appear twice in the NT in the noun form apostasia, (Acts 21:21; 2 Thes 2:3) and here in Heb 3:12 in the verb form aphistemi, (translated here as ‘departing,’ but in some other translations as ‘turn away’). The Greek term literally means ‘standing away’ from God and refers to abandoning what one has previously believed and experienced in Christ. It involves a disowning of Christ and departure from the body of Christ and the Christian faith. Apostasy is the consequence of a deliberate and volitional choice to ‘[depart] from the living God’ (3:12).
(1) Individual apostasy is possible only for those who have first experienced the blood of the new covenant in regeneration and sanctification, renewal through the Holy Spirit and relationship with Christ (cf. Heb 6:4-5; 10:29). The Christian faith is primarily about relationship to God. Thus the Bible speaks of God’s fatherhood and Christ’s sonship, and our relationship to God as His family and children (Rom 8:14-17). Whereas logical systems of thought and natural law are cold, fixed and unrelational, salvation in Christ is personal, relational and requires our responsiveness. God’s grace in His Son makes possible our relationship with Him and is sufficient for sustaining it. In Jesus’ analogy about the vine and the branches (John 15:1-8), the believer (BRANCH) who remains in relational union with Christ (VINE) is secure and has life. Should a believer because of hardness of heart ever choose to break this relational grace-union with Christ and thereby ‘depart’ that person may in the end perish eternally as an unbeliever (John 15:6).
(2) The Bible issues urgent warnings about this grave possibility, designed both to alert us to the deadly danger of abandoning our union with Christ and to motivate us to persevere in faith and obedience. The divine purpose of these warning passages must not be weakened by the view that states, ‘the warnings are real, but the possibility of actual apostasy is not.’ Rather, we must see these warnings as speaking to the reality of our probationary period, and we should regard them with alarm if we want to be saved in the end. A few of the many NT warning passages are: Mat 24:4-5, 11-13; Luke 12:46; John 15:6; Rom 11:17-21; 1 Cor 15:2; Col 1:23; 1 Tim 4:1, 16; 2 Tim 4:2-5; Heb 2:1-3; 3:7-19; 4:1, 6-7, 11; 6:4-9; 10:26-31; 12:25; 2 Pet 1:10; 2:20-22.
(3) Examples of actual apostasy can be found in Ex 32; 2 Ki 17:7-23; Ps 106; Is 1:2-4; Jer 2:1-9; Acts 1:25; Gal 5:4; 1 Tim 1:18-20; 2 Pet 2:1, 15, 20-22; Jude 4, 11-13; see article on The Age of the Antichrist, p. 1912, for comments on apostasy predicted to occur within the professing church in the last days of this age.
(4) The steps that lead to apostasy are as follows:
(a) Believers, through unbelief, fail to take the truths, exhortations, warnings, promises and teachings of God’s Word with utmost seriousness (Mark 1:15; Luke 8:13; John 5:44,47; 8:46).
(b) If the realities of the world become greater than the realities of God’s heavenly kingdom, believers gradually cease to draw near to God through Christ (Heb 4:16; 7:19,25; 11:6).
(c) Through the deceitfulness of sin, they become increasingly tolerant of sin in their own lives (1 Cor 6:9-10; Eph 5:5; Heb 3:13). They no longer love righteousness and hate wickedness (see Heb 1:9, note).
(d) Through hardness of heart (Heb 3:8,13) and rejecting God’s way (Heb 3:10), they ignore the repeated voice and rebuke of the Holy Spirit (Eph 4:30; 1 Thes 5:19-22).
(e) The Holy Spirit is grieved (Eph 4:30; cf. Heb 3:7-8) and His fire put out (1 Thes 5:19) and His temple violated (1 Cor 3:16). He eventually departs from the former believers (Judg 16:20; Ps 51:11; Rom 8:13; 1 Cor 3:16-17; Heb 3:14).
(5) If backsliding continues on its course unchecked, individuals may eventually reach the point when no second beginning is possible. (a) Those who once had a saving experience with Christ but deliberately and continually harden their hearts to the Spirit’s voice (Heb 3:7-19), continue to sin willfully (Heb 10:26), and refuse to repent and return to God may reach a point of no return where repentance is no longer possible (Heb 6:4-6; see Deut 29:18-21, note; 1 Sam 2:25, note; Prov 29:1, note). There is a limit to God’s patience (see 1 Sam 3:11-14; Mat 12:31-32; 2 Thes 2:9-11; Heb 10:26-29,31; 1 John 5:16). (b) This point of no return cannot be defined in advance. Therefore, the only safeguard against the danger of ultimate apostasy is found in the admonition: ‘Today, if ye will hear his voice, harden not your hearts’ (Heb 3:7-8,15, 4:7).
(6) It must be emphasized that while backsliding is a danger for all who drift from the faith (Heb 2:1-3), apostasy does not occur without constant and willful sinning against the voice of the Holy Spirit (see Mat 12:31, note on sin against the Holy Spirit). The person whose heart is truly hardened by sin may then calculatingly choose to turn away from God (Heb 3:12).
(7) Those who genuinely become concerned about their spiritual condition and find in their hearts the desire to return to God in repentance have sure evidence that they have not committed the unpardonable sin or apostasy (Heb 6:4-6). Scripture clearly affirms that God does not want anyone to perish (2 Pet 3:9; cf. Is 1:18-19; 55:6-7) and declares that God joyfully receives the prodigal who repents and returns to Him (Luke 15:11-24; cf. Gal. 5:4 with 4:19; 1 Cor 5:1-5 with 2 Cor 2:5-11; see also Rom 11:20-23; Jas 5:19-20; Rev 3:14-20; note the example of Peter, Mat 16:16; 26:74-75; John 21:15-22).
Taken from http://arminiantheologyblog.wordpress.com/2012/09/26/individual-apostasy/