Prevenient grace - Does grace only make it possible to believe?

Does God only enable faith? Does grace stop there, and then we make a decision?
 
John 1:7  He came as a witness to testify concerning that light, so that through him all men might believe.
Certainly grace does enable belief, and Jesus came to provide grace, required grace, without which we could not believe. But more is implied in such verses as these:
 
John 12:32  But I, when I am lifted up from the earth, will draw all men to myself.
 
Romans 5:15  But the gift is not like the trespass. For if the many died by the trespass of the one man, how much more did God's grace and the gift that came by the grace of the one man, Jesus Christ, overflow to the many!
 
Luke 15:4 Suppose one of you has a hundred sheep and loses one of them. Does he not leave the ninety-nine in the open country and go after the lost sheep until he finds it?
 
Not until he either finds it or gives up.
 
Luke 15:5  And when he finds it...
 
Galatians 1:15-16  But when God, who set me apart from birth and called me by his grace, was pleased  16 to reveal his Son in me...
 
And "those he called, he justified..." (Rom. 8:30).

But does this verse indicate that grace may not accomplish its purpose in salvation?
 
2 Corinthians 6:1  As God's fellow workers we urge you not to receive God's grace in vain.
But it seems he is addressing believers:
 
2 Corinthians 7:1  Since we have these promises, dear friends, let us purify ourselves from everything that contaminates body and spirit, perfecting holiness out of reverence for God.
 
So then the question becomes not whether saving grace ever fails, but whether people can lose their salvation, which is another topic...