Objection 1. It seems that no one may be blotted out of the book of life. For Augustine says (De Civ. Dei xx, 15): "God's foreknowledge, which cannot be deceived, is the book of life." But nothing can be taken away from the foreknowledge of God, nor from predestination. Therefore neither can anyone be blotted out from the book of life.
Objection 2. Further, whatever is in a thing is in it according to the disposition of that thing. But the book of life is something eternal and immutable. Therefore whatsoever is written therein, is there not in a temporary way, but immovably, and indelibly.
Objection 3. Further, blotting out is the contrary to inscription. But nobody can be written a second time in the book of life. Neither therefore can he be blotted out.
On the contrary, It is said, "Let them be blotted out from the book of the living" (Psalm 68:29).
I answer that, Some have said that none could be blotted out of the book of life as a matter of fact, but only in the opinion of men. For it is customary in the Scriptures to say that something is done when it becomes known. Thus some are said to be written in the book of life, inasmuch as men think they are written therein, on account of the present righteousness they see in them; but when it becomes evident, either in this world or in the next, that they have fallen from that state of righteousness, they are then said to be blotted out. And thus a gloss explains the passage: "Let them be blotted out of the book of the living." But because not to be blotted out of the book of life is placed among the rewards of the just, according to the text, "He that shall overcome, shall thus be clothed in white garments, and I will not blot his name out of the book of life" (Apocalypse 3:5) (and what is promised to holy men, is not merely something in the opinion of men), it can therefore be said that to be blotted out, and not blotted out, of the book of life is not only to be referred to the opinion of man, but to the reality of the fact. For the book of life is the inscription of those ordained to eternal life, to which one is directed from two sources; namely, from predestination, which direction never fails, and from grace; for whoever has grace, by this very fact becomes fitted for eternal life. This direction fails sometimes; because some are directed by possessing grace, to obtain eternal life, yet they fail to obtain it through mortal sin. Therefore those who are ordained to possess eternal life through divine predestination are written down in the book of life simply, because they are written therein to have eternal life in reality; such are never blotted out from the book of life. Those, however, who are ordained to eternal life, not through divine predestination, but through grace, are said to be written in the book of life not simply, but relatively, for they are written therein not to have eternal life in itself, but in its cause only. Yet though these latter can be said to be blotted out of the book of life, this blotting out must not be referred to God, as if God foreknew a thing, and afterwards knew it not; but to the thing known, namely, because God knows one is first ordained to eternal life, and afterwards not ordained when he falls from grace.
Reply to Objection 1. The act of blotting out does not refer to the book of life as regards God's foreknowledge, as if in God there were any change; but as regards things foreknown, which can change.
Reply to Objection 2. Although things are immutably in God, yet in themselves they are subject to change. To this it is that the blotting out of the book of life refers.
Reply to Objection 3. The way in which one is said to be blotted out of the book of life is that in which one is said to be written therein anew; either in the opinion of men, or because he begins again to have relation towards eternal life through grace; which also is included in the knowledge of God, although not anew.
Source: Summa Theologica (New Advent)