Peter warns the believers against "false prophets" (2 Peter 2:1) who were previously righteous, but then turned into...
Accursed children! Forsaking the right way, they have gone astray. -- 2 Peter 2:14-15
For if, after they have escaped the defilements of the world through the knowledge of our Lord and Savior Jesus Christ, they are again entangled in them and overcome, the last state has become worse for them than the first. For it would have been better for them never to have known the way of righteousness than after knowing it to turn back from the holy commandment delivered to them. -- 2 Peter 2:20-21
Paul also warned believers who were already saved:
Take care, brothers, lest there be in any of you an evil, unbelieving heart, leading you to fall away from the living God. -- Hebrews 3:12
The Greek word ἀφίστημι translated as "fall away" means (according to the Thayer's Greek Lexicon):
to make stand off, cause to withdraw, to remove; tropically, to excite to revolt
In other words it is possible for believers to lose faith and to "withdraw" or to "remove" their salvation.
A typical symptom of an unbelieving person is to try to earn salvation by keeping the laws. Paul warns the Galatians that they should not disregard Christ' salvation for unnecessary laws that they feel obliged to keep. The believers had to choose if they had "faith" that Christ's sacrifice was sufficient or whether their salvation would come from keeping the laws:
For freedom Christ has set us free; stand firm therefore, and do not submit again to a yoke of slavery. Look: I, Paul, say to you that if you accept circumcision, Christ will be of no advantage to you. I testify again to every man who accepts circumcision that he is obligated to keep the whole law. You are severed from Christ, you who would be justified by the law; you have fallen away from grace. For through the Spirit, by faith, we ourselves eagerly wait for the hope of righteousness. For in Christ Jesus neither circumcision nor uncircumcision counts for anything, but only faith working through love. -- Galatians 5:1-6 (ESV)
On the other hand, you also get people who think God's grace is enough so that they may to live the lawless life.
And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’
Although Simon believed and were baptised (Acts 8:13), he continued to live in the bond of iniquity:
"You have neither part nor lot in this matter, for your heart is not right before God. Repent, therefore, of this wickedness of yours, and pray to the Lord that, if possible, the intent of your heart may be forgiven you. For I see that you are in the gall of bitterness and in the bond of iniquity." -- Acts 8:21-23 (ESV)
This was also Peter's understanding where he taught how to "supplement your faith" so that you will "never fall".
For this very reason, make every effort to supplement your faith
- with virtue, and
- virtue with knowledge, and
- knowledge with self-control, and
- self-control with steadfastness, and
- steadfastness with godliness, and
- godliness with brotherly affection, and
- brotherly affection with love.
For if these qualities are yours and are increasing, they keep you from being ineffective or unfruitful in the knowledge of our Lord Jesus Christ. For whoever lacks these qualities is so nearsighted that he is blind, having forgotten that he was cleansed from his former sins. Therefore, brothers, be all the more diligent to confirm your calling and election, for if you practice these qualities you will never fall. -- 2 Peter 1:5-10 (ESV)
Jesus himself compared believers (not churches or denominations) with branches that could get "pruned":
“I am the true vine, and my Father is the vinedresser. Every branch in me that does not bear fruit he takes away, and every branch that does bear fruit he prunes, that it may bear more fruit. -- John 15:1-2
If anyone does not abide in me he is thrown away like a branch and withers; and the branches are gathered, thrown into the fire, and burned. -- John 15:6
Paul compare the believer's life with a race:
Do you not know that in a race all the runners run, but only one receives the prize? So run that you may obtain it. Every athlete exercises self-control in all things. They do it to receive a perishable wreath, but we an imperishable. So I do not run aimlessly; I do not box as one beating the air. But I discipline my body and keep it under control, lest after preaching to others I myself should be disqualified. -- 1 Corinthians 9:24-27 (ESV)
“Who are kept by the power of God through faith unto salvation ready to be revealed in the last time” -- I Peter 1:5
Out of context it seems like Peter wrote that "the power of God will keep us into salvation". This is not what Peter wrote.
The key here is "through faith". God will never force you to do anything, neither will he brainwash you to "have faith".
“My sheep know my voice, and I know them, and they follow me; and I give unto them eternal life; and they shall never perish, and no one shall snatch them out of my hand” -- John 10:27-28
Out of context it seems like that it is Jesus' responsibility to make sure nobody gets lost. This is not what Jesus said. The key here is "they follow me". Salvation does not stop when after you got repented. You should keep following Jesus or you will get lost (moving out of Jesus' protection).
In addition to this Matthew also recorded:
If a man has a hundred sheep, and one of them has gone astray, does he not leave the ninety-nine on the mountains and go in search of the one that went astray? And if he finds it, truly, I say to you, he rejoices over it more than over the ninety-nine that never went astray. So it is not the will of my Father who is in heaven that one of these little ones should perish. -- Matthew 18:12-14
Jesus pointed out that it is not his Father's will that anyone should perish, he does not say "no one will ever perish". If it was not possible for anyone to "perish" then this last sentence would be unnecessary.
The hope that this passage gives us, is that whenever we do go "astray" He will "search" for us. We still have a chance and a choice to go back and ask for forgiveness, because it is not the Father's will that anyone should perish.