Objection 1. It would seem that there is hope in the damned. For the devil is damned and prince of the damned, according to Matthew 25:41: "Depart... you cursed, into everlasting fire, which was prepared for the devil and his angels." But the devil has hope, according to Job 40:28, "Behold his hope shall fail him." Therefore it seems that the damned have hope.
Objection 2. Further, just as faith is either living or dead, so is hope. But lifeless faith can be in the devils and the damned, according to James 2:19: "The devils... believe and tremble." Therefore it seems that lifeless hope also can be in the damned.
Objection 3. Further, after death there accrues to man no merit or demerit that he had not before, according to Ecclesiastes 11:3, "If the tree fall to the south, or to the north, in what place soever it shall fall, there shall it be." Now many who are damned, in this life hoped and never despaired. Therefore they will hope in the future life also.
On the contrary, Hope causes joy, according to Romans 12:12, "Rejoicing in hope." Now the damned have no joy, but sorrow and grief, according to Isaiah 65:14, "My servants shall praise for joyfulness of heart, and you shall cry for sorrow of heart, and shall howl for grief of spirit." Therefore no hope is in the damned.
I answer that, Just as it is a condition of happiness that the will should find rest therein, so is it a condition of punishment, that what is inflicted in punishment, should go against the will. Now that which is not known can neither be restful nor repugnant to the will: wherefore Augustine says (Gen. ad lit. xi, 17) that the angels could not be perfectly happy in their first state before their confirmation, or unhappy before their fall, since they had no foreknowledge of what would happen to them. For perfect and true happiness requires that one should be certain of being happy for ever, else the will would not rest.
In like manner, since the everlastingness of damnation is a necessary condition of the punishment of the damned, it would not be truly penal unless it went against the will; and this would be impossible if they were ignorant of the everlastingness of their damnation. Hence it belongs to the unhappy state of the damned, that they should know that they cannot by any means escape from damnation and obtain happiness. Wherefore it is written (Job 15:22): "He believeth not that he may return from darkness to light." It is, therefore, evident that they cannot apprehend happiness as a possible good, as neither can the blessed apprehend it as a future good. Consequently there is no hope either in the blessed or in the damned. On the other hand, hope can be in wayfarers, whether of this life or in purgatory, because in either case they apprehend happiness as a future possible thing.
Reply to Objection 1. As Gregory says (Moral. xxxiii, 20) this is said of the devil as regards his members, whose hope will fail utterly: or, if it be understood of the devil himself, it may refer to the hope whereby he expects to vanquish the saints, in which sense we read just before (Job 40:18): "He trusteth that the Jordan may run into his mouth": this is not, however, the hope of which we are speaking.
Reply to Objection 2. As Augustine says (Enchiridion viii), "faith is about things, bad or good, past, present, or future, one's own or another's; whereas hope is only about good things, future and concerning oneself." Hence it is possible for lifeless faith to be in the damned, but not hope, since the Divine goods are not for them future possible things, but far removed from them.
Reply to Objection 3. Lack of hope in the damned does not change their demerit, as neither does the voiding of hope in the blessed increase their merit: but both these things are due to the change in their respective states.
Source: Summa Theologica (New Advent)