To answer your question, I think we have to clarify the issue.  We are all born into this world in a condition of sin, and barring the radical intervention of God's Grace, that's the condition in which we will live out our lives and in which we will die.  BUT--God provides the grace that enables us to respond to him in faith, and when we do, we move positionally from the world into the family of God.  Salvation is a choice:  we either accept the gift freely offered by God, or we do not.  If you accept God's gift, you are "born again"--that is, your sins are forgiven, you become a member of God's family and you begin living a new life in Christ, a life as God's son or daughter.

And once in the family, is there anything you can do to make you not a member of the family?  I would argue, no.  You may well behave in a way that dishonors the family and God; you may well grow bored with the family and drift away; or you may even grow angry and bitter and storm out of the house!  But you are still a son or a daughter of God.  That doesn't change:  your fellowship with God may change, but your position in the family does not.

That's what the story of the Prodigal Son is all about (Luke 15: 11-32).  Even though the youngest son has an honored place in the family, he choses to turn his back on his father and leave, demanding his inheritance.  We're never told why the son behaves like this:  perhaps he's bored; perhaps he's angry; or perhaps he's simply rebellious.  In any case, the father allows him to walk out the door.  And sure enough, as soon as the son steps into the world he gets into trouble, squandering his fortune, disgracing his family and father, and ending up in a pig pen (a horrible place for a nice Jewish boy!).  Notice that the father never chases after him, never tries to coax him home.  The son has made a choice; the father respects his son's choice; and the father takes his hands off, allowing his son to walk away.  But all the while his son is gone, the father waits at the window, watching the road, knowing that his son will return.

Meanwhile--in the pig pen--the son has a change of heart:  "When he came to his senses, he said, 'How many of my father's hired men have food to spare, and here I am starving to death!  I will set out and go back to my father and say to him:  Father, I have sinned against heaven and against you.  I am no longer worthy to be called your son; make me like one of your hired men.'  So he got up and went to his father" (Luke 15: 17-20).  And the father welcomes him with opened arms.

Even though you are "born again" as a member of the family of God, like the Prodigal Son you may walk away from the family, and the Father will respect your decision:  he will not stop you.  But even while you're away, you are still a son or a daughter.  You may even end up in a pig pen!  But even there, you are still a son or a daughter--and I'll tell you this:  you won't be happy in that pig pen, because you're not a pig; you're a son.   After a while you will come to your senses, and you will arise and go home to your Father.  And he will be there, waiting for you with opened arms.

I've told this story in class, and I invariably have someone ask:  "But what would happen if the son had died in the pig pen?"  My answer:  then he would be a dead son, not a dead pig.  And the Father would come and take him home.

You see the distinction?  Once God accepts us into the family as one of his own, there is nothing we can do to not be his son or daughter.  Membership in the family is positional.  You can fall out of fellowship with God, yes; but you can never lose your position within the family.