Apostasy is a deliberate abandonment of faith. Several New Testament passages (Hebrews 6:4-6, 10:26, 2 Peter 2:20-21) seem to say that someone who has fallen away from Christian faith has no chance to repent and come back. These passages have been interpreted many different ways, and it is fair to say than no one is really sure of their original intent.
In their original context, these were warnings, in the strongest possible terms, to the first century Christians not to abandon their new faith because of persecution or false teachings. Thus, the authors may have used some hyperbole (exaggeration) to emphasize the point. [Jesus also used hyperbole for emphasis (Matthew 7:3-5, Mark 10:25).]
If these verses really mean that a person who has fallen away has no chance to repent, that would seem to contradict many other New Testament teachings about God's mercy and constant willingness to forgive. These verses are probably not directed at people who have doubts or who lose their faith and come back later. It is the person who deliberately, permanently and hard-heartedly rejects faith who will never repent, and thus can never be forgiven.
Hebrews 6:4-6 (NIV)
4 It is impossible for those who have once been enlightened, who have tasted the heavenly gift, who have shared in the Holy Spirit, 5 who have tasted the goodness of the word of God and the powers of the coming age 6 and who have fallen[a] away, to be brought back to repentance. To their loss they are crucifying the Son of God all over again and subjecting him to public disgrace.
Hebrews 10:26 (NIV)
26 If we deliberately keep on sinning after we have received the knowledge of the truth, no sacrifice for sins is left,
2 Peter 2:20-21 (NIV)
20 If they have escaped the corruption of the world by knowing our Lord and Savior Jesus Christ and are again entangled in it and are overcome, they are worse off at the end than they were at the beginning. 21 It would have been better for them not to have known the way of righteousness, than to have known it and then to turn their backs on the sacred command that was passed on to them.