"And Revelation has been constantly rejected in the course of history by the very same Churches to which it was purportedly addressed. The only seven somethings that had ever received it constantly throughout human history are the Romans, whose city Rome is founded upon seven hills; and where Satan was enthroned (Revelation 2:13). This fact is not without reason, since the Romans seem to have been very fond of Apocalyptic writings generally: whether John's, or Peter's, or Hermas' Shephard, or Ezra's. (see the Muratory Canon, for instance; and remember that IV Ezra was part of Catholic Bibles up until the age of Trent, when 3rd and 4th Ezra weren't included). The fact that it was rejected by the very same cities to which it was supposed to have been written to is also of signifficance: the excuse for that is that some or certain heretics used it and abused it at a certain point in time"
LVKA doesn't make much of an effort to support his claims. And we aren't told why a book would have to be "constantly" accepted in order for us to accept it. If Revelation was widely accepted early on, but became less accepted later, why should the later status of the book be of much concern to us when making a judgment about its canonicity?
Revelation is different from some other Biblical books in that it's addressed to seven churches rather than one individual or one church, for example. The initial audience of seven churches creates more opportunity for verification or falsification of the book's canonicity. And unfortunately for LVKA's argument, the evidence from those churches points in the opposite direction of what he's suggesting. The data we have concerning the seven churches of Revelation 2-3 suggests that they initially accepted the book rather than rejecting it.
Some of the seven churches were prominent in early church history, and Christians from other locations were often in contact with these churches. For example, Ignatius writes to a few of the churches, some of the most prominent church leaders of the early patristic era came from those churches (Polycarp, Melito, Polycrates, etc.), some of those church's leaders traveled and communicated widely (Polycarp's visit to Rome, etc.), and Irenaeus cites the churches of Smyrna and Ephesus as two of the most significant churches of his day (Against Heresies, 3:3:4). If the seven churches of Asia Minor had rejected the book of Revelation, they were in a position to make that rejection widely known and to influence other churches and individuals to reject the book as well.
But the evidence suggests that, instead, Revelation was widely accepted:
"As early as the middle of the second century, Revelation was ascribed to John, 'one of the apostles of Christ' (Justin, Dial. 81). Other second-century works and writers make the same claim: a lost commentary on Revelation by Melito, bishop of Sardis (c. A.D. 165; see Eusebius, H.E. 4.26.2); Irenaeus (c. 180; Adv. Haer. 3.11.1, 4.20.11, 4.35.2); and the Muratorian Canon (late second century). Whether Papias, an even earlier witness than these (d.c. 130), can be added to this list is disputed, but a good case can be made out that he both knew Revelation and attributed it to John. The evidence of these writers is particularly strong in that two of them (three, if Papias is included) could well be reporting firsthand evidence. Sardis, where Melito was bishop, was one of the churches addressed in Revelation (1:11; 3:1-6). Irenaeus was from Smyrna, also a church addressed in Revelation (1:11; 2:8-11), and claims to have heard Polycarp, who had talked with John the apostle himself. Papias knew John the apostle personally. The early tradition is confirmed by the third-century fathers Tertullian, Hippolytus, and Origen. Not only do these authors ascribe Revelation to John the apostle, they do so without any hint of there being a contrary claim. No New Testament book, concludes Gerhard Maier, has a stronger or earlier tradition about its authorship than does Revelation." (D.A. Carson, et al., An Introduction To The New Testament [Grand Rapids, Michigan: Zondervan, 1992], p. 468)
I would change some of the wording or add some qualifiers that Carson, Moo, and Morris don't mention, but the general thrust of their assessment is accurate. Other sources could be added to theirs, both in terms of authorship attribution and in terms of citations of the book as scripture. See, for example, Bruce Metzger's discussion of Clement of Alexandria, Cyprian, and other relevant sources in The Canon Of The New Testament (New York: Oxford University Press, 1997).
The claim would sometimes be made that the heretic Cerinthus authored Revelation, and later sources would speculate about authorship by some other John. But neither argument seems to have been prominent early on, and such claims are rarely even mentioned among the early sources.
Irenaeus refers to manuscripts of Revelation that were "ancient" in his day and how the correct text of a passage in Revelation was confirmed by "those men who saw John face to face" (Against Heresies, 5:30:1). Multiple eyewitnesses of the apostle John were still living when Revelation was circulating, and it was circulating long enough for them to be involved in commenting on the textual discrepancy Irenaeus references. The view of Revelation held by Irenaeus and his contemporaries was influenced by earlier sources.
"We have also churches which are nurselings of John's: for although Marcion disallows his Apocalypse, yet the succession of their bishops, when traced back to its origin, will be found to rest in John as originator." (Against Marcion, 4:5)
Tertullian isn't addressing the authorship of Revelation. He's addressing the apostolic origin of the churches of Revelation 2-3. But his comments imply that those churches accepted Revelation. It's unlikely that Tertullian would mention Marcion's rejection of Revelation only to go on to appeal to some churches that also rejected the book. Tertullian accepted Revelation himself, and his comments about the seven churches involve a claim to be knowledgeable about the history of those churches. It's unlikely that Tertullian would accept Revelation if he knew that the book was rejected by those seven churches. And it's unlikely that Tertullian would be ignorant of a rejection of Revelation by those churches, if they did reject it, especially given his claim to be so familiar with the history of the churches. Similarly, it's unlikely that men such as Irenaeus and Origen, who traveled and communicated so widely and showed such an interest in those churches, would be ignorant of their rejection of Revelation or would know of it, yet accept Revelation anyway.