St. Augustine was not primarily talking about the Eucharist when he said that Jesus "commended to us His Body." Instead, this venerable saint was referring to the holy catholic Church. For, as St. Paul says, the Church is the Body of Christ and Christ Himself is its head (see Romans 12 & 1 Corinthians 12).
Clearly for St. Paul and St. Augustine, "Body of Christ" is not metaphorical; and it is not a fancy way of talking about "church." Rather, this phrase describes yet one more aspect of Our Blessed Lord Jesus. To say it simply, the same Body which was born of the ever-Virgin Mary; the same Body which suffered death on the cross and was raised from the dead; the same Body which we consume at the altar during Holy Communion—that same Body is the Church. Into that Body we were incorporated through Holy Baptism, and apart from that Body we cannot live the Christian life. For Jesus says, "Apart from Me" (that is, apart from My Body) "you can do nothing" (John 15.5; see also Psalm 16.2).
Since the Church is the Body of Christ, it would be heretical to say that this Body is only invisible and has no visible form. For Our Lord Jesus, who became flesh for our sakes, is not invisible now. His ascension did not mean the removal of His human nature—His flesh and bones. Neither did it mean that He simply became invisible. For, unlike the angels, one of the chief characteristics of our bodies is that they can, and will always, be seen. In fact, that is a chief aspect to us being made "in the image of God." For Christ is the image of God; which means that He is the only visible, tangible Person of the Trinity that becomes creature; and we are made in His image, which means our visibility conforms to Him, and not Him to us.
So when Our Lord ascended, His body did not vanish or get taken off. Rather, it was gloriously transformed. And this was done for two reasons: first, so that we could be united in Him (baptism) and Him in us (Eucharist) by the Sacraments. And secondly, so that He—the virgin born—could be visibly present throughout the world in His Church.
This is profound, and not easy to understand. However, it is important to our understanding of "church." For we might tempted to believe that the church is defined strictly in human terms—an assembly of believers. But St. Paul and St. Augustine urge us never to forget that the primary definition and understanding of "church" is rooted in Christ. It is His Body, not our association. And it is His Body, not merely a group of people who believe and practice the same thing.
Because this is hard for us to understand and remember, the danger is that we flay Jesus' skin from His Body, and think and talk only in terms of an "invisible church" or "a unity that cannot be seen." But if Our Lord Jesus is still in His flesh, and if the Church is His Body, then His Church must be visibly present—visible even to the eyes of the unbelievers. (For remember, even the unbelievers saw Jesus with their eyes, although they did not see or confess Him as the Christ.)
The question, now, is "where is Christ's Body the Church visibly present"? Or, to use St. Augustine's words, where does the Body He commended to us continue to lie?
We Lutherans are in the habit of saying that Our Lord's Body continues to lie where the Word is purely preached and the Sacraments are rightly given. But, historically, a more "meaty" and "fleshly" answer is this: the church is the communion fellowship between those pastors (bishops and priests) who hold steadfastly to the Jesus who is both God and Man, sacrificed on the cross and now given from the altar.
If that communion fellowship between the pastors is broken by false doctrine or false worship, is that any longer the holy and glorified Body of Christ?
And is one member or portion of that Body in danger if it remains in a communion fellowship with pastors who deny the Faith once delivered?
From the latter part of "Addendum IV."