In 1 Timothy 4:14, the warning is to avoid neglecting the gift that was given to the reader. In Hebrews 8:9 the neglect or ignorance was God’s approach to the people of the exodus who did not continue in his covenant. Matthew 22:5 however, seems to shed some light on the Hebrews 2:3 passage where there is a picture of a neglectful attitude toward salvation. In this passage, Jesus shares a parable of a king who gave a wedding feast for his son. Everything was ready, but when the servants went out with the invitation, the people paid them no attention—the messengers were rejected, turned away, treated poorly, and in some cases even killed. The king was angered by this reaction so he sent his troops to kill those who murdered his messengers and then he had their cities burned. Eventually, the king sent his messengers into the streets to invite anybody the messengers could find.
The author of Hebrews is cautioning his readers not to neglect this message for he knows the consequences are grave. But he is not acting as if he has received this invitation and that is the end of it. He includes himself in the warning saying, “We must pay much closer attention to what we have heard, lest we drift away from it” (Hebrews 2:1, ESV). It seems that paying much closer attention is to understand the details. And it also seems that we need to follow this warning to the extent that the author takes it, later writing, “Take care, brothers, lest there be any of you of an evil, unbelieving heart, leading you to fall away from the living God. But exhort one another every day, as long as it is called ‘today,’ that none of you may be hardened by the deceitfulness of sin” (Hebrews 3:12-3, ESV). Paying much closer attention would appear to be an ongoing thing; and being an ongoing thing, it seems that neglecting the message of salvation and the blessing that come from it is a very serious matter.
This warning in Hebrews 3:12, is a warning to be cautious and even avoid having an unbelieving heart. This unbelieving heart the author warns about, it seems, is evil and can cause one to fall away from, or even rebel against the Living God. In verse 13, the reader is encouraged to exhort one another daily to avoid the hardening of the heart caused by sin. Genesis 8:21 says, “ the intention of man’s heart is evil from his youth” (ESV) and Deuteronomy 11:6 warns “Take care lest your heart be deceived, and you turn aside and serve other gods and worship them” (ESV). Therefore, it seems that the default or natural desire of the human heart is toward this hardened state, and this hardness causes our faith in, and love for God to be less than our 'all' as Deuteronomy 6, 10, 13, and 30 instruct (which Jesus teaches as recorded in the Gospels of Matthew, Mark, and Luke.)
Hebrews 3:13 shows that the way to avoid this frightful hardening is to engage in daily exhortation with, and among other Christian believers of the living God. (In light of Hebrews 1 and 2, this faith should be in Jesus, to be more specific.) It is a daily effort in study, prayer, discussion, openness, honesty, and accountability with the other believers that fights the natural desire of the ever-hardening, sinful heart. This will hopefully help the reader follow the instruction of Hebrews 3:14 to “hold our original confidence firm to the end” (ESV).
In addition, this message was written to believers so while it could be a discussion about completely forfeiting salvation after one is regenerated (or born again), it is a strong possibly that is is about missing out on the many good things God has for his people.
While verses 12 and 13 are counted in Chapter 3, they seem to fit better heading into Chapter 4 because the call to take courage and keep the heart soft and faithful is compared to God’s people who stepped in faith to leave Egypt but eventually sinned by turning from God. They eventually took their faith and placed it elsewhere, in other words, they allowed their hearts to return to the default hardness and unbelief of all God was doing for them. While they still counted themselves as God's people, they did not trust that he had their best interests in mind. The result of this sin was a prohibition of the blessings and rest found in the Promised Land. The author continues to compare rest (or lack thereof) to the condition of the heart, and those with no rest had hard hearts. The author is encouraging the readers (then and now) to take caution and avoid the same pitfalls of those who did not remain completely faithful to the end.
Strong, James, John R. Kohlenberger, James A. Swanson, and James Strong. The Strongest Strong's Exhaustive Concordance of the Bible. Grand Rapids, Mich: Zondervan, 2001.