This article compares the views of Augustine to those of John Owen on the question of the Perseverance of the Saints. http://johnowen.org/media/knapp_on_augustine_and_owen.pdf

Augustine and Owen each believed that it is solely by God's grace that one is given the gift of perseverance to the end, and that is the defining characteristic of the elect. Each believed that the church is filled with the elect, with hypocrites who pretend to be believers yet are not, and a middle category of people. Members of this third group have received a form of grace from God that produces in them some holiness and faith and benefit of Christianity and capability to advance God's work through the church. This form is not hypocrisy but is genuine, but they do not persevere, hence are not among the elect.

Both Augustine and Owen taught that the Scriptural warnings against falling away are a means by which God keeps the elect on track or brings them back from a temporary backsliding, not proof that the elect may lose their salvation. Though the article does not cite 1 Cor 8:11 specifically, Owen in his lengthy treatises against Arminianism addressed it using this approach. (See "The Works of John Owen, Volume 10, page 468. http://www.prayermeetings.org/files/John_Owen/Owen_V10_Arminianism_Death_Of_Christ_Divine_Justice.pdf)

A quote from Owen concerning 1 Corinthians 8:11:

2. But let us see a second place, which is <460811>1 Corinthians 8:11, “And through thy knowledge shall thy weak brother perish, for whom Christ died.” This seemeth to have more color, but really yieldeth no more strength to the persuasion for whose confirmation it is produced, than the former. A brother is said to perish for whom Christ died. That by perishing here is understood eternal destruction and damnation, I cannot apprehend. That which the apostle intimates whereby it is done, is eating of things offered to an idol, with conscience or regard of an idol, by the example of others who pretended to know that an idol was nothing, and so to eat freely of the things offered to them. That so doing was a sin in its own nature damnable, none can doubt. All sin is so; every time we sin, for anything that lieth in us, we perish, we are destroyed. So did the eater of things offered to idols. But that God always revengeth sin with damnation on all in whom it is, we deny; he hath otherwise revealed himself in the blood of Jesus Christ. That every such a one did actually perish eternally, as well as meritoriously, cannot be proved. Besides, he that is said to perish is called a brother, — that is, a believer; we are brethren only by faith, whereby we come to have one Father. As he is said to be a brother, so Christ is said to die for him. That a true believer cannot finally perish may easily be proved; therefore, he who doth perish is manifestly declared never to have been any: “They went out from us, because they were not of us.” If any perish, then, he was never a true believer. How, then, is he said to be a brother? Because he is so in profession, so in our judgment and persuasion; it being meet for us to think so of them all. As he is said to be a brother, so Christ is said to die for him, even in that judgment which the Scripture allows to us of men. We cannot count a man a brother, and not esteem that Christ died for him; we have no brotherhood with reprobates. Christ died for all believers, John 17. So we esteem all men walking in the due profession of the gospel, not manifesting the contrary; yet of these, that many may perish none ever denied. Farther; this, so shall he perish, referreth to the sin of him that layeth the offense; for aught that lieth in him, he ruins him irrecoverably. Hence see their argument: — “The apostle telleth persons walking offensively, that by this abusing their liberty, others will follow them, to the wounding of their conscience and ruin, who are brethren, acknowledged so by you, and such as for whom Christ died: therefore, Christ died for all the reprobates in the world. ‘Is it just and equal,’ saith the apostle, ‘that ye should do such things as will be stumbling-blocks in the way of the weak brother, at which he might stumble and fall?’ therefore, Christ died for all.” We do not deny but that some may perish, and that eternally, concerning whom we ought to judge that Christ died for them, whilst they live and converse with us according to the nile of the gospel.

Augustine and Owen disagree on one important point. Augustine did not believe that it was possible for a Christian to know with assurance that they were among the elect unless God, by special revelation given to only a few, tells them so. He says this is so that the elect may not fall into pride. Owen, however, believed that the objective fact of a person's election would manifest itself in a subjective experience of assurance that could be a useful assistance to a believer in helping them to persevere.

The importance of Augustine's contribution is that there are Catholic views of perseverance and the elect not being subject to losing their salvation that do not rely upon the Reformed views, such as those from Calvinism. John Owen was a firm Calvinist, and the continiuity of thought between Ausgustine and Owen in most regards offers a defense of the idea of perseverance broader than just a Calvinistic position.

A quote from the article:

Although Augustine’s writings have caused some confusion on this point, his views on this issue are quite explicit; he firmly maintained that each and every one of the elect had received the gift of perseverance from God, and that they cannot ultimately lose their salvation. Augustine speaks directly about the elect numerous times in De correptione et gratia and occasionally in De dono perseverantiae. After addressing the necessity of admonitions in De correptione et gratia, Augustine asserts that the gift of perseverance is assuredly given to the elect and, on account of that gift, they cannot ultimately fall away from grace.

The answer to Paul's question :

Shall the weak brother perish ? (I Corinthians 8:11 - KJV - απολειται ο ασθενων αδελφος)

is ... no he shall not perish.

The reason that the weak brother will not perish is :

... for whom Christ died. (I Corinthians 8:11 - KJV - δι ον χριστος απεθανεν)

The brother will not perish (or 'be destroyed') because Christ died for him and Jesus Christ loves him and Jesus Christ will not permit the sin of one brother to cause the other - weak - brother to be overcome and to be cast away.

Thus He sends a messenger to instruct both the 'strong' brother and the 'weak' brother - and we have the documented record of the messenger's epistle, proof positive that Jesus Christ is risen, and ascended, and ministers as a Priest at the right hand of the Father in the heavens.

And thus Paul addresses the errant - 'strong' - brother (so full of his superior knowledge and so sure of his own 'strength') and questions him. Because of you and your superior knowledge, will you damage your brother ?

Will you cast a stumbling block - a 'scandal' - in his path ? Will you trust in your own strength of knowledge and care nothing for the weaker composure of your brother who will be tempted to do what is - actually - against his own conscience ?

For the weak brother might be emboldened to follow suit but, afterwards, his conscience will smite him (for his knowledge is not strong) and he will be overcome of guilt.

And Paul questions him to the ultimate - because of you and your attitude, will this brother ultimately perish ? Will he commit sin against his own conscience and be overcome of guilt and be destroyed ?

But the question of that weak brother's ultimate destiny is not up to the errant 'strong' brother.

Nor is up to the weakness of himself (else would we all perish).

It is ultimately a matter of what God, in Christ, will or will not do.

For the Lord (I Peter 3:9) is not slack ... but is long-suffering to us-ward (that is to say to the 'them', also, who have obtained like precious faith with 'us' - see I Peter 1:1) not willing that any should perish, but that all should come to repentance.

[And I do respect what (I think) prompts the OP question - that repentance is necessary, else we perish. And I do not respect the attitude of those who think that a knowledge of doctrine is carte blanche to commit sin.]

The Lord is not slack. He sees every sparrow which drops to the ground in the forest, Matthew 10:29. He knows the number of the hairs of the head of them that seek him, Luke 12:7. He is aware of every single thought - not one is withheld from him, Job 42:2.

And he will not let one single one perish, for whom sacrifice was made and for whom righteousness has been satisfied . . . it cannot be.

Otherwise, righteousness would be no more righteousness.

Note : I do not subscribe to 'tulip' myself. Jack Glass, in Glasgow, conveyed it to me fifty years ago when I was seventeen but I found it to be not a sufficiently spiritual expression of the gospel for me to embrace it. But I have answered the question as one who believes that the sufferings and death of Jesus Christ are effectual and are not dependent on the works of men to supplement them.

But I do believe that all for whom Jesus Christ suffered and died shall be brought to repentance and shall be brought to faith and that they shall be fully justified and, ultimately, glorified.

And in that, some might call me a follower of John Calvin and I would not disagree.

I would say that the argument of the posed question falls down because the argument has left Jesus Christ out of the process and has considered only the two brothers and their relevant 'strength' and 'weakness'.

It is the Lord who is above all.