Although the story of the criminal on the cross demonstrates that last-minute conversions are possible, the Bible warns us to repent now, without waiting another moment. John the Baptist warned, “Repent, for the kingdom of heaven is at hand” (Matthew 3:2). Jesus had the identical message concerning the need for immediate repentance, “Repent, for the kingdom of heaven is at hand” (Matthew 4:17).
The Bible warns us concerning the brevity of the human lifespan. “You are just a vapor that appears for a little while and then vanishes away” (James 4:14). We are not instructed to consider converting someday, but to believe today! “Today if you hear his voice, do not harden your hearts” (Hebrews 3:7-8, 14; 4:7). None of us knows how much time we have left in this life or what the circumstances of our death will be. We may die in a sudden, unexpected manner that will preclude a deathbed conversion. The only reasonable option is to repent and believe in Jesus Christ today.
Many people die without having the experience of an extended amount of time on a death bed. Many people die instantly and unexpectedly, with no opportunity to trust in Christ. 2 Corinthians 6:2 declares, "In the time of my favor I heard you, and in the day of salvation I helped you. I tell you, now is the time of God's favor, now is the day of salvation."
Read more: http://www.gotquestions.org/death-bed-conversion.html