"I will never cast out" is Jesus' statement of absolute assurance that He will not cast out those who come to Him in humble repentance, no matter the sin.

As John Bunyan so greatly illustrated:

• Are you a great, old, hard-hearted, or backsliding sinner, but you come to Christ?
  Jesus says, "I will never cast you out."
• Are you a sinner who has served Satan all your days, but you come to Christ?
  Jesus says, "I will never cast you out."
• Are you a sinner who has sinned against light and mercy, but you come to Christ?
  Jesus says, "I will never cast you out."
• Are you a sinner who has no good thing to bring with you, but you come to Christ?
  Jesus says, "I will never cast you out."

And Dane Ortluand captures the heart of the Father and the Son in this verse:

• All - "Once the Father sets his loving gaze on a wandering sinner, that sinner's rescue is certain."
• the Father - "Our redemption is not a matter of a gracious Son trying to calm down an uncontrably angry Father. The Father himself ordains our deliverance. He takes the loving initiative."
• gives - "It is the Father's deep delight to freely entrust recalcitrant rebels into the gracious care of his Son."
• will come - "God's saving purpose for a sinner is never thwarted. He is never frustrated. He never runs out of resources. If the Father calls us, we will come to Christ."
• and whoever comes - "Yet we are not robots. While the Father is clearly the sovereign overseer of our redemption, we are not dragged kicking and screaming into Christ against our will. Divine grace is so radical that it reaches down and turns around our very desires. Our eyes are opened. Christ becomes beautiful. We come to him. And anyone -- 'whoever' -- is welcome. Come and welcome to Jesus Christ."
• comes to me - "We do not come to a set of doctrines. We do not come to a church. We do not even come to the gospel. All these are vital. But most truly, we come to a person, to Christ himself."

What this verse captures is not about our perseverance. It is about Christ's perseverance -- the perseverance of the heart of Christ towards all who the Father has given to the Son, all who have come to Christ.