"You are permitted to understand the secrets of the Kingdom of Heaven, but others are not. To those who listen to my teaching, more understanding will be given, and they will have an abundance of knowledge. But for those who are not listening, even what little understanding they have will be taken away from them." (Matthew 13:11-12)
It is possible to be exposed to the Bible all your life and understand nothing. Jesus explains that those who hear but don't listen (meaning they don't apply the teaching to their own life) become hardened. They become so good at ignoring what the Bible is saying that there comes the point where they no longer CAN hear. It is a terrifying thought that people can get so calloused to the things of God that they will not and cannot hear.
In the book of Revelation, God sent plagues and other trials to get people to repent. Several times, however, we are told the people still refused to repent even after seeing the power of God displayed.
How do we guard against this? First, read and listen to what the Bible tells us. Second, take what you read personally. Read trying to listen for what God is saying to you. Third, take action on what you read. Finally, confess your sin to Him truthfully and with repentance. To keep secret areas of your life from God (yes, that is as stupid as it sounds) facilitates the hardening process. Keep your heart soft through honest confession. Open yourself to His truth and the life that comes from that truth.