Apparently this Steve Anderson, who is promoting the OSAS doctrine has never read in the book of Revelation where Jesus speaks to the churches. In particular, to the church of Sardis.
Rev. 3:5 "He that overcometh the same shall be clothed in white raiment, and I will not blot out his name out of the book of life, but I will confess his name before my Father and before his angels".
Because those in the church in Sardis would not have their names blotted out of the Book of Life, it remains that those who were not overcoming, would have their names blotted out of the Book of Life.
It is quite obvious through the NT and OT writings, that you can believe, and yet, if you don't walk out your salvation through sanctification, then you will not receive eternal life.
Salvation is a free gift, but our gratitude in receiving such an amazing gift, causes us to sanctify our lives unto the Lord, so that our name will stay written in the Lamb's Book of Life.