Does Walking Close to Christ Ensure Holiness?

Walking close to Christ does not ensure holiness.

No. Judas Iscariot stole, betrayed, & committed suicide. Peter denied Christ.

If walking close to Christ does not ensure holiness, then how can we be holy as Christ is holy?

Our holiness is not our own. It is Christ's holiness which he gives us.

Christ freely gives his holiness to those who realize their holiness is not enough and ask him for it. They will then, because they are born of the Spirit of God receive his holiness and walk in step with him.

Does this mean the child of God will always walk consistently perfect? No. The child of God is still human and though they now have the power to live as a child of God, sometimes they will fall. The key is in whom they've trusted and their response having understood their humanity.