Whee, an art history thread!
So first of all, the thing is that what we call "realism"(in quotes because defining something as realistic is always a "relative to what" game and in any case what constitutes "realism" is rather iffy), that is the kind of optical-geometric verism that developed in renaissance Europe is not at all a universal standard for defining artistic quality simply because it was not regarded as a goal.
With that dispensed with, let's move on to the development of late antique art. So the first key point is that many aspects of the classical tradition did in fact persist for a very long time-the development of a modelled painting continued well into the christian era and to a great degree into the Umayyad epoch. Likewise, much classical iconography was extra-ordinarily persistent into the christian era. What we are looking at is rather a shift in the manner of artistic representation-it's different, not worse. Now there are several different ways to read this. We could read it as a shift in orientation to clarity of narrative, as some do-that is, the goal of an artist is to more clearly render narrative(this is most important in book production and mosaic). We could also read it as emphasizing the development of an art that emphasized seeing over touching or the illusion of touchability (sometimes called "Optic" versus "Haptic"), or a need to move past one set of artistic problems that demands a total reorganization of artistic methods. The point is that late antique art is built around creating a new set of approaches to art-making that were demanded by the changed circumstances of social life and that for this reason it can hardly be called a failed attempt at classical art(which in any case IIRC had long since collapsed into mechanical reproduction of existing methods). For further discussion of the formation of late antique art, and what would be required to prevent it, I would suggest reading Panofsky's Perspective as Symbolic Form, the catalog to the recent exhibition of early Byzantine art at the Metropolitan("Byzantium and Islam"), Reigl's Late Roman Art Industry, and anything by Kurt Weitzmann on the topic, although doubtless a specialist in classical or late antique art would be able to provide a much more up-to-date bibliography.
Now having said all that, there was considerable variation in the technical quality of late antique art that correlates more or less with the relative wealth of the patrons, the abilities of the artists involved, whether or not the art was from a metropolitan and provinical center, and so on and so forth. If you wish to simply preserve the relative technical competence of a specific region or group of artists, that is more or less a reasonable and doable goal.
Errnge: Wait, what? Medival art is not a decline(or at least the sheer virtuosity of a work like the sculpture of Atun, the Ramsey Psalter's masterful and certain draughtsmanship, or the wit of marginal illumination, and most places in Europe were plenty rich to hire good artists.
EDIT: Because it's rude to not illustrate what you are talking about, here are some specimen major works of late antique art:
http://en.wikipedia.org/wiki/File:Spas_vsederzhitel_sinay.jpg
http://commons.wikimedia.org/wiki/Category:Vienna_Genesis
http://en.wikipedia.org/wiki/File:Diptych_Barberini_Louvre_OA9063_whole.jpg
http://en.wikipedia.org/wiki/File:ViennaDioscoridesPlant.jpg