I think God can only make that call. I think Paul seems to think someone could be cut off from Christ once saved. In Romans 11 Paul talks about what happens when one comes to faith in Christ, enters the family, Jew and Gentile, depicted as a cultivated olive tree.
Romans 11
16 For if the firstfruit is holy, the lump is also holy; and if the root is holy, so are the branches. 17 And if some of the branches were broken off, and you, being a wild olive tree, were grafted in among them (Gentile Christians who are grafted in the tree, picture of salvation, entering into the tree, entering God's family through Christ), and with them became a partaker of the root and fatness of the olive tree, 18 do not boast against the branches. But if you do boast, remember that you do not support the root, but the root supports you.
19 You will say then, “Branches were broken off that I might be grafted in.” 20 Well said. Because of unbelief they were broken off, and you stand by faith. Do not be haughty, but fear. 21 For if God did not spare the natural branches, He may not spare you either. (Seems to me these wild grafted in branch can be broken off). 22 Therefore consider the goodness and severity of God: on those who fell, severity; but toward you, goodness,[f] if you continue in His goodness. Otherwise you also will be cut off. 23 And they also, if they do not continue in unbelief, will be grafted in, for God is able to graft them in again. 24 For if you were cut out of the olive tree which is wild by nature, and were grafted contrary to nature into a cultivated olive tree, how much more will these, who are natural branches, be grafted into their own olive tree?
To me the bible seems to teach that if we remain/abide (1 John 2:28) in Christ we are eternally secure.
IMHO, being born again is a spiritual idea which depicts a person from moving from outside God's family to inside His family, Paul refers to this as our adoption, sonship. Can someone completely reject Christ after believing in Him? Yes, I've heard of many who walked away from the faith. The book of 1 John, John gives 6 ways to know that we are saved:
1) We have the right doctrine regarding Christ (His deity and God's son, in the flesh, He is our atonement) what the disciples first taught) (the reason John wrote this book because of the confusion the Gnostics were teaching) (1 john 1:1-4, 2 John 2:22, 1 John 4:2-3, 1 John 4:14-15)
2) We Obey Christ's commands. We practice righteousness, we don't continue in willful sin (1 John 1:6, 1 John 2:3-6, 1 John 2:29, 1 John 3:4-10, 1 John 3:24, 1 John 5:18)
3) We love our brothers and sisters in Christ, we love God. (1 John 2:9-10, 1 John 3-11-23, 1 John 4:7-12, 1 John 4:17-19, 1 John 4:20-21)
4) We do not follow the world (1 John 2:15-17)
5) His Spirit testifies to our spirit. (1 John 4:6-13)
6) God answers our prayers
(**according to HIS WILL** and the answer is not always YES!) (1 John 5:14)