Objection 1. It would seem that anyone may merit perseverance. For what a man obtains by asking, can come under the merit of anyone that is in grace. Now men obtain perseverance by asking it of God; otherwise it would be useless to ask it of God in the petitions of the Lord's Prayer, as Augustine says (De Dono Persev. ii). Therefore perseverance may come under the merit of whoever has grace.
Objection 2. Further, it is more not to be able to sin than not to sin. But not to be able to sin comes under merit, for we merit eternal life, of which impeccability is an essential part. Much more, therefore, may we merit not to sin, i.e. to persevere.
Objection 3. Further, increase of grace is greater than perseverance in the grace we already possess. But a man may merit an increase of grace, as was stated above (Article 8). Much more, therefore, may he merit perseverance in the grace he has already.
On the contrary, What we merit, we obtain from God, unless it is hindered by sin. Now many have meritorious works, who do not obtain perseverance; nor can it be urged that this takes place because of the impediment of sin, since sin itself is opposed to perseverance; and thus if anyone were to merit perseverance, God would not permit him to fall into sin. Hence perseverance does not come under merit.
I answer that, Since man's free-will is naturally flexible towards good and evil, there are two ways of obtaining from God perseverance in good: first, inasmuch as free-will is determined to good by consummate grace, which will be in glory; secondly, on the part of the Divine motion, which inclines man to good unto the end. Now as explained above (6,7,8), that which is related as a term to the free-will's movement directed to God the mover, falls under human merit; and not what is related to the aforesaid movement as principle. Hence it is clear that the perseverance of glory which is the term of the aforesaid movement falls under merit; but perseverance of the wayfarer does not fall under merit, since it depends solely on the Divine motion, which is the principle of all merit. Now God freely bestows the good of perseverance, on whomsoever He bestows it.
Reply to Objection 1. We impetrate in prayer things that we do not merit, since God hears sinners who beseech the pardon of their sins, which they do not merit, as appears from Augustine [Tract. xliv in Joan.] on John 11:31, "Now we know that God doth not hear sinners," otherwise it would have been useless for the publican to say: "O God, be merciful to me a sinner," Luke 18:13. So too may we impetrate of God in prayer the grace of perseverance either for ourselves or for others, although it does not fall under merit.
Reply to Objection 2. The perseverance which is in heaven is compared as term to the free-will's movement; not so, the perseverance of the wayfarer, for the reason given in the body of the article.
In the same way may we answer the third objection which concerns the increase of grace, as was explained above.
Source: Summa Theologica (New Advent)