Objection 1. It would seem that despair does not arise from sloth. Because different causes do not give rise to one same effect. Now despair of the future life arises from lust, according to Gregory (Moral. xxxi, 45). Therefore it does not arise from sloth.
Objection 2. Further, just as despair is contrary to hope, so is sloth contrary to spiritual joy. But spiritual joy arises from hope, according to Romans 12:12, "rejoicing in hope." Therefore sloth arises from despair, and not vice versa.
Objection 3. Further, contrary effects have contrary causes. Now hope, the contrary of which is despair, seems to proceed from the consideration of Divine favors, especially the Incarnation, for Augustine says (De Trin. xiii, 10): "Nothing was so necessary to raise our hope, than that we should be shown how much God loves us. Now what greater proof could we have of this than that God's Son should deign to unite Himself to our nature?" Therefore despair arises rather from the neglect of the above consideration than from sloth.
On the contrary, Gregory (Moral. xxxi, 45) reckons despair among the effects of sloth.
I answer that, As stated above (17, 1; I-II, 40, 1), the object of hope is a good, difficult but possible to obtain by oneself or by another. Consequently the hope of obtaining happiness may be lacking in a person in two ways: first, through his not deeming it an arduous good; secondly, through his deeming it impossible to obtain either by himself, or by another. Now, the fact that spiritual goods taste good to us no more, or seem to be goods of no great account, is chiefly due to our affections being infected with the love of bodily pleasures, among which, sexual pleasures hold the first place: for the love of those pleasures leads man to have a distaste for spiritual things, and not to hope for them as arduous goods. On this way despair is caused by lust.
On the other hand, the fact that a man deems an arduous good impossible to obtain, either by himself or by another, is due to his being over downcast, because when this state of mind dominates his affections, it seems to him that he will never be able to rise to any good. And since sloth is a sadness that casts down the spirit, in this way despair is born of sloth.
Now this is the proper object of hope--that the thing is possible, because the good and the arduous regard other passions also. Hence despair is born of sloth in a more special way: though it may arise from lust, for the reason given above.
This suffices for the Reply to the First Objection.
Reply to Objection 2. According to the Philosopher (Rhet. i, 11), just as hope gives rise to joy, so, when a man is joyful he has greater hope: and, accordingly, those who are sorrowful fall the more easily into despair, according to 2 Corinthians 2:7: "Lest... such an one be swallowed up by overmuch sorrow." Yet, since the object of hope is good, to which the appetite tends naturally, and which it shuns, not naturally but only on account of some supervening obstacle, it follows that, more directly, hope gives birth to joy, while on the contrary despair is born of sorrow.
Reply to Objection 3. This very neglect to consider the Divine favors arises from sloth. For when a man is influenced by a certain passion he considers chiefly the things which pertain to that passion: so that a man who is full of sorrow does not easily think of great and joyful things, but only of sad things, unless by a great effort he turn his thoughts away from sadness.
Source: Summa Theologica (New Advent)