In reading about Tertullian I don't see any real substantive argument against him except that he didn't like some of the customs of the Church. I'd have to study it more but he sounds like the first Protestant to be perfectly honest.
Ireaneus has another quote:
"For that there is nothing whatever openly, expressly, and without controversy said in any part of Scripture respecting the Father conceived of by those who hold a contrary opinion, they themselves testify, when they maintain that the Saviour privately taught these same things not to all, but to certain only of His disciples who could comprehend them, and who understood what was intended by Him through means of arguments, enigmas, and parables."
Iraeneus-Against Heresy, Book II
Then you must not have come across his argument that souls can "endure as long as God wills them to endure" (perseverant autem quoadusque eas Deus et esse, et perseverare voluerit).
In other words, his argument is that the soul is not itself a life: it must be given life.And that which is given is outside of the self, its nature. Only God is Life itself (Adversus haereses II, 34).
Like I said, you need to get your facts straight, HD.
Clement of Alexandria, who was a Platonist, admits that the soul was not immortal "by nature" (hinc apparet quoniam non est naturaliter anima incorruptibilis, Adumbrationes, I Petri 1:9) .
+Jerome states "I do not say, indeed, that all souls die."
If Man from the beginning had chosen things immortal, in obedience to God's commandments, he would have been rewarded with immortality and have become God, "an adoptive God," deus assumptus, Theos anadihthis (+Theophilus of Antioch, Ad Autolycum II, 24 and 27).
"The soul is not in itself immortal, O Greeks, but mortal. Yet it is possible for it not to die" (Tatian, Oratio ad Graecos, 13).
Blessed Augustine qualifies the immortality of the soul to be given by God: Anima hominis immortalis est secundum quendam modum suum; non enim omni modo sicut Deus (Epist. VFF, ad Hieronymum (and is therefore not by its nature itself life), and he also states in two instances (Jo., tr. 23, 9; cf. De Trinitate, 19.15, and De Civ. Dei, 19.3) that the soul is mortal according to the mutability of this life (mortalis in quantum mutabilis).
+John of Damascus states that even Angels are not immortal by nature, but only by grace (Exact Exposition of the Orthodox Faith II, 3)
[T]hat "intellectual beings are not immortal by nature" [but only by the grace of God] (+Sophronius, the Patriarch of Jerusalem, VI Ecumenical Council, 681 AD)