Chris Date (CD) has a video in which he claims that Clement of Rome held to "conditional immortality" (link - if you're interested to hear what he has to say about Clement of Rome, you can jump forward to timestamp 26:00 and listen to 44:09).
First, note that we refer to the book we refer to as 1 Clement, a letter from the church at Rome to the church at Corinth, is traditionally identified as having been written by Clement of Rome, even though Clement may not have written the letter or may not have done so in an individual capacity. The author of the book avoids using the first person to refer to himself, does not identify himself as Clement in the text of the work, and the letter begins, "The Church of God which sojourneth in Rome to the Church of God which sojourneth in Corinth...." Likewise, the postscript of the letter asks that the messengers (who presumably carried the letter) be speedily returned to "us." Although the author of 1 Clement is traditionally identified as Clement of Rome, I will refer to the author as "the author of 1 Clement."
At least one other letter has been attributed to Clement of Rome (it's referred to as 2 Clement), but it is by another author. The mid-second century author of that work does refer to "eternal punishment" (2 Clement 6:7), affirms that the dead will be judged (2 Clement 1:1), uses "death" to refer to something like spiritual death ("our whole life was nothing else but death" 2 Clement 1:6), suggests that the fire of the afterlife will have a hardening effect like fire has on clay with the effect of repentance being impossible there (2 Clement 8:1-3), and identifies the punishment of the damned with "grievous torments in unquenchable fire" (2 Clement 17:7) after quoting from Isaiah 66:24 (2 Clement 17:5). Naturally, CD does not provide his detailed comments on this work, and he does not need to, since it is not the work of Clement of Rome. I merely mention it as a minor aside against the false and ridiculous notion that the doctrine of eternal conscious torment should be associated with Augustine, centuries later despite being the understanding of Christians before then.
Returning to 1 Clement, the full text of the epistle in the original Greek and parallel English can be found at the following link (link to full text of 1 Clement).
While Hell is not the central focus of the letter, the author of 1 Clement, does touch on the subject a little.
XI. Διὰ φιλοξενίαν καὶ εὐσέβειαν Λὼτ ἐσώθη ἐκ Σοδόμων, τῆς περιχώρου πάσης κριθείσης διὰ πυρὸς καὶ θείου, πρόδηλον ποιήσας ὁ δεσπότης ὅτι τοὺς ἐλπίζοντας ἐπ’ αὐτὸν οὐκ ἐγκαταλείπει, τοὺς δὲ ἑτεροκλινεῖς ὑπάρχοντας εἰς κόλασιν καὶ αἰκισμὸν τίθησιν. 2. Συνεξελθούσης γὰρ αὐτῷ τῆς γυναικὸς ἑτερογνώμονος ὑπαρχούσης καὶ οὐκ ἐν ὁμονοίᾳ, εἰς τοῦτο σημεῖον ἐτέθη, ὥστε γενέσθαι αὐτὴν στήλην ἁλὸς ἕως τῆς ἡμέρας ταύτης, εἰς τὸ γνωστὸν εἶναι πᾶσιν ὅτι οἱ δίψυχοι καὶ οἱ διστάζοντες περὶ τῆς τοῦ Θεοῦ δυνάμεως εἰς κρίμα καὶ εἰς σημείωσιν πάσαις ταῖς γενεαῖς γίνονται.
11. For his hospitality and godliness Lot was saved from Sodom, when all the country round about was judged by fire and brimstone; the Master having thus fore shown that He forsaketh not them which set their hope on Him, but appointeth unto punishment and torment them which swerve aside. [2.] For when his wife had gone forth with him, being otherwise minded and not in accord, she was appointed for a sign hereunto, so that she became a pillar of salt unto this day, that it might be known unto all men that they which are double-minded and they which doubt concerning the power of God are set for a judgment and for a token unto all the generations.
The author of 1 Clement argues that God has appointed unbelievers to "κόλασιν καὶ αἰκισμὸν" (punishment and torture). Even if we were to accept annihilationist claims that kolasin can refer to a death penalty, as such (and that seems to be a stretch at best), aikismon is not similarly ambiguous: it means torture not death. Moreover, the author of 1 Clement links these punishments and tortures with the fire and brimstone (πυρὸς καὶ θείου) that was put on Sodom.
Furthermore, the author of 1 Clement suggests a perpetuity to the judgment by saying that the judgment will be "unto all generations" like Lot's wife who "unto this day" is a pillar of salt.
Because CD has convinced himself to reduce the punishment of Sodom to annihilation, he fails to account for the "torment" aspect of the comment. Indeed, eternal conscious torment fits much better both with "punishment" and "torment." Likewise, while one can certainly appreciate that the memory of a death can serve as a reminder, the ongoing existence of Lot's wife as a pillar of salt suggests an emphasis on the damned continuing to exist in some form so that they serve a similar memorial function.
What remains to be said? The author of 1 Clement does not explicitly say that the torment will last forever. So, if someone wants to claim that 1 Clement does not rule out the idea that the torment might end some day, I think it's fair to acknowledge that 1 Clement does not directly address this topic.
That said, because the author of 1 Clement focuses on the punishments and torture of the wicked, 1 Clement is not consistent with the annihilationist focus on cessation of being as the reward of the wicked.
CD argues from 1 Clement 9 that capital punishment (a term the author of 1 Clement never uses) awaits the wicked. That section reads as follows:
IX. Διὸ ὑπακούσωμεν τῇ μεγαλοπρεπεῖ καὶ ἐνδόξῳ βουλήσει αὐτοῦ, καὶ ἱκέται γενόμενοι τοῦ ἐλέους καὶ τῆς χρηστότητος αὐτοῦ προσπέσωμεν καὶ ἐπιστρέψωμεν ἐπὶ τοὺς οἰκτιρμοὺς αὐτοῦ, ἀπολιπόντες τὴν ματαιοπονίαν τήν τε ἔριν καὶ τὸ εἰς θάνατον ἄγον ζῆλος. 2. Ἀτενίσωμεν εἰς τοὺς τελείως λειτουργήσαντας τῇ μεγαλοπρεπεῖ δόξῃ αὐτοῦ. 3. Λάβωμεν Ἐνώχ, ὃς ἐν ὑπακοῇ δίκαιος εὑρεθεὶς μετετέθη, καὶ οὐχ εὑρέθη αὐτοῦ θάνατος. 4. Νῶε πιστὸς εὑρεθεὶς διὰ τῆς λειτουργίας αὐτοῦ παλιγγενεσίαν κόσμῳ ἐκήρυξεν, καὶ διέσωσεν δι’ αὐτοῦ ὁ δεσπότης τὰ εἰσελθόντα ἐν ὁμονοίᾳ ζῷα εἰς τὴν κιβωτόν.
9. Wherefore let us be obedient unto His excellent and glorious will; and presenting ourselves as suppliants of His mercy and goodness, let us fall down before Him and betake ourselves unto His compassions, forsaking the vain toil and the strife and the jealousy which leadeth unto death. [2.] Let us fix our eyes on them that ministered perfectly unto His excellent glory. [3.] Let us set before us Enoch, who being found righteous in obedience was translated, and his death was not found. [4.] Noah, being found faithful, by his ministration preached regeneration unto the world, and through him the Master saved the living creatures that entered into the ark in concord.
CD is not wrong that the author of 1 Clement has in mind death as a consequence of sin. However, the death that the author of 1 Clement uses as an illustration is the ordinary death that we all eventually face, and that even Noah himself eventually faced. Thus, "capital punishment" as a description is a spin too far.
CD argues that the author of 1 Clement uses "death" in simply the ordinary way. This is inaccurate. First, the author of 1 Clement uses "death" in a way that also seems to refer to spiritual death in his quotation of "death into the world" (1 Clement 3). Moreover, this usage is particularly relevant, because it links jealousy with death: "seeing that they have conceived an unrighteous and ungodly jealousy, through which also death entered into the world" (ζῆλον ἄδικον καὶ ἀσεβῆ ἀνειληφότας, δι’ οὗ καὶ «θάνατος εἰσῆλθεν εἰς τὸν κόσμον». 1 Clement 3) This word for jealousy is, of course, the same Greek word used in 1 Clement 9.
Moreover, jealousy is what the author of 1 Clement identifies as a critical problem in Corinth. Thus, jealousy is discussed in 1 Clement 3, and then repeatedly in 1 Clement 4, 5, and 6. The author of 1 Clement comes back to jealousy in 1 Clement 9, 14, 43 and 45. Finally, the author of 1 Clement brings up jealousy one last time in the conclusion at 1 Clement 63.
Perhaps even more significantly than the jealousy-death connection in general, the author of 1 Clement states at 1 Clement 4: "Jealousy caused Joseph to be persecuted even unto death, and to come even unto bondage." (Ζῆλος ἐποίησεν Ἰωσὴφ μέχρι θανάτου διωχθῆναι καὶ μέχρι δουλείας εἰσελθεῖν.)
We know, and it seems fair to assume the author of 1 Clement knew, that Joseph was not literally persecuted to physical death, but instead to an imprisonment. In case you are wondering, it's not because a different Greek word for death is used: it's the same Greek word for death.
CD presents six other examples of this word use in the text, which falsely suggests that the author of 1 Clement only uses the word in one particular way.
Moreover, the translation CD provided for 1 Clement 51 seems inaccurate and misleading in the context of our discussion.
LI. Ὅσα οὖν παρεπέσαμεν καὶ ἐποιήσαμεν διά τινας παρεμπτώσεις τοῦ ἀντικειμένου, ἀξιώσωμεν ἀφεθῆναι ἡμῖν· καὶ ἐκεῖνοι δέ, οἵτινες ἀρχηγοὶ στάσεως καὶ διχοστασίας ἐγενήθησαν, ὀφείλουσιν τὸ κοινὸν τῆς ἐλπίδος σκοπεῖν. 2. Οἱ γὰρ μετὰ φόβου καὶ ἀγάπης πολιτευόμενοι ἑαυτοὺς θέλουσιν μᾶλλον αἰκίαις περιπίπτειν ἢ τοὺς πλησίον· μᾶλλον δὲ ἑαυτῶν κατάγνωσιν φέρουσιν ἢ τῆς παραδεδομένης ἡμῖν καλῶς καὶ δικαίως ὁμοφωνίας. 3. Καλὸν γὰρ ἀνθρώπῳ ἐξομολογεῖσθαι περὶ τῶν παραπτωμάτων ἢ σκληρῦναι τὴν καρδίαν αὐτοῦ, καθὼς ἐσκληρύνθη ἡ καρδία τῶν στασιασάντων πρὸς τὸν θεράποντα τοῦ Θεοῦ Μωϋσῆν, ὧν τὸ κρίμα πρόδηλον ἐγενήθη. 4. «Κατέβησαν γὰρ εἰς ᾅδου ζῶντες», καὶ «θάνατος ποιμανεῖ αὐτούς». 5. Φαραὼ καὶ ἡ στρατιὰ αὐτοῦ καὶ πάντες οἱ ἡγούμενοι Αἰγύπτου, «τά τε ἅρματα καὶ οἱ ἀναβάται» αὐτῶν οὐ δι’ ἄλλην τινὰ αἰτίαν ἐβυθίσθησαν εἰς θάλασσαν ἐρυθρὰν καὶ ἀπώλοντο, ἀλλὰ διὰ τὸ σκληρυνθῆναι αὐτῶν τὰς ἀσυνέτους καρδίας μετὰ τὸ γενέσθαι τὰ σημεῖα καὶ τὰ τέρατα ἐν Αἰγύπτῳ διὰ τοῦ θεράποντος τοῦ Θεοῦ Μωϋσέως.
51. For all our transgressions which we have committed through any of the wiles of the adversary, let us entreat that we may obtain forgiveness. Yea and they also, who set themselves up as leaders of faction and division, ought to look to the common ground of hope. [2.] For such as walk in fear and love desire that they themselves should fall into suffering rather than their neighbors; and they pronounce condemnation against themselves rather than against the harmony which hath been handed down to us nobly and righteously. [3.] For it is good for a man to make confession of his trespasses rather than to harden his heart, as the heart of those was hardened who made sedition against Moses the servant of God; [4.] whose condemnation was clearly manifest, for they went down to hades alive, and Death shall be their shepherd. [5.] Pharaoh and his host and all the rulers of Egypt, their chariots and their horsemen, were overwhelmed in the depths of the Red Sea, and perished for none other reason but because their foolish hearts were hardened after that the signs and the wonders had been wrought in the land of Egypt by the hand of Moses the servant of God.
- William Burton (1647) translated: "punishment and plagues" (link at XIV in Burton's sectioning of the text)
- William Wake (1719) translated: "punishment and correction" (link)
- Temple Chevallier (1833) translated: "punishment and correction" (link)
- John Keith (1897) included in Schaff's edition: "punishment and torture" (link)
- Kevin Edgecomb (2006) translated: "punishment and torments" (link)
- Adolf von Harnack (English ed. and trans. Jacob Cerone) (2021) translated: "punishment and torment" (p. 15)