Objection 1. It would seem that despair is not a sin. For every sin includes conversion to a mutable good, together with aversion from the immutable good, as Augustine states (De Lib. Arb. ii, 19). But despair includes no conversion to a mutable good. Therefore it is not a sin.
Objection 2. Further, that which grows from a good root, seems to be no sin, because "a good tree cannot bring forth evil fruit" (Matthew 7:18). Now despair seems to grow from a good root, viz. fear of God, or from horror at the greatness of one's own sins. Therefore despair is not a sin.
Objection 3. Further, if despair were a sin, it would be a sin also for the damned to despair. But this is not imputed to them as their fault but as part of their damnation. Therefore neither is it imputed to wayfarers as their fault, so that it is not a sin.
On the contrary, That which leads men to sin, seems not only to be a sin itself, but a source of sins. Now such is despair, for the Apostle says of certain men (Ephesians 4:19): "Who, despairing, have given themselves up to lasciviousness, unto the working of all uncleanness and [Vulgate: 'unto'] covetousness." Therefore despair is not only a sin but also the origin of other sins.
I answer that, According to the Philosopher (Ethic. vi, 2) affirmation and negation in the intellect correspond to search and avoidance in the appetite; while truth and falsehood in the intellect correspond to good and evil in the appetite. Consequently every appetitive movement which is conformed to a true intellect, is good in itself, while every appetitive movement which is conformed to a false intellect is evil in itself and sinful. Now the true opinion of the intellect about God is that from Him comes salvation to mankind, and pardon to sinners, according to Ezekiel 18:23, "I desire not the death of the sinner, but that he should be converted, and live" [Vulgate: 'Is it My will that a sinner should die... and not that he should be converted and live?' Cf. Ezekiel 33:11: while it is a false opinion that He refuses pardon to the repentant sinner, or that He does not turn sinners to Himself by sanctifying grace. Therefore, just as the movement of hope, which is in conformity with the true opinion, is praiseworthy and virtuous, so the contrary movement of despair, which is in conformity with the false opinion about God, is vicious and sinful.
Reply to Objection 1. In every mortal sin there is, in some way, aversion from the immutable good, and conversion to a mutable good, but not always in the same way. Because, since the theological virtues have God for their object, the sins which are contrary to them, such as hatred of God, despair and unbelief, consist principally in aversion from the immutable good; but, consequently, they imply conversion to a mutable good, in so far as the soul that is a deserter from God, must necessarily turn to other things. Other sins, however, consist principally in conversion to a mutable good, and, consequently, in aversion from the immutable good: because the fornicator intends, not to depart from God, but to enjoy carnal pleasure, the result of which is that he departs from God.
Reply to Objection 2. A thing may grow from a virtuous root in two ways: first, directly and on the part of the virtue itself; even as an act proceeds from a habit: and in this way no sin can grow from a virtuous root, for in this sense Augustine declared (De Lib. Arb. ii, 18,19) that "no man makes evil use of virtue." Secondly, a thing proceeds from a virtue indirectly, or is occasioned by a virtue, and in this way nothing hinders a sin proceeding from a virtue: thus sometimes men pride themselves of their virtues, according to Augustine (Ep. ccxi): "Pride lies in wait for good works that they may die." On this way fear of God or horror of one's own sins may lead to despair, in so far as man makes evil use of those good things, by allowing them to be an occasion of despair.
Reply to Objection 3. The damned are outside the pale of hope on account of the impossibility of returning to happiness: hence it is not imputed to them that they hope not, but it is a part of their damnation. Even so, it would be no sin for a wayfarer to despair of obtaining that which he had no natural capacity for obtaining, or which was not due to be obtained by him; for instance, if a physician were to despair of healing some sick man, or if anyone were to despair of ever becoming rich.
Source: Summa Theologica (New Advent)