They did; it's just that most of them have been lost to time, weather, and armies. Probably the best-preserved examples of Roman painting are the murals at Pompeii, Herculaneum, Stabiae, and Opis(discussed here
http://www.art-and-archaeology.com/roman/painting.html) and the mummy portraits from Faiyum(see
http://en.wikipedia.org/wiki/Fayum_mummy_portraits), as well as various descriptions of lost paintings by artists like Apelles in Pliny's Natural History. Perserving this tradition uninterrupted would likely require one of the following: the lack of a Byzantine collapse in Syria or the survivial of a more Syrian-oriented caliphate so the Classical tradition is not overtaken by the more Persian manner that was coming to dominate under the Abbasids and the Selujiks. In Western Europe you probably need an earlier growth of parchment manuscripts because panels just don't survive well in cold and wet climates and possibly the Franks having more mss. in the style of, say, the Vienna Genesis(very different that high classical roman painting, but about what you can realistically expect given the massive artistic shifts in the late antique world).
If you instead mean "why do the extant classical paintings discussed above not fit the Renaissance model", that's a different discussion and one that likely requires far more intensive research; I'll see what I have time to plow through. Possible reasons to start from include the development of Christian pictorial cycles, the emergence first of tempera and then of oil as a medium, the love of fine detail that comes from the International Gothic style and the growth of manuscript painting in that style, and the mathematical development of geometry that drove so much Italian painting.