I'd start by qualifying the notion of a "slave economy": there was an important slave sector, but Scheidel argues persuasively that slaves were never much more than around a tenth of the population: even doubling his Italian rural slaves in line with traditional (though insecurely-founded) estimates, it seems difficult to raise the proportion much above his upper-bound 13%. Assuming a similar urban population and allowing for an urban slave overlap between the two categories, close to 80% of the Empire's population had to consist of non-slave rural inhabitants in greater or lesser degrees of subjection: it was necessarily a peasant-based economy.

But even maintaining Scheidel's 5-8 million slaves required annual replacement of a quarter of a million or more, by capture, purchase or reproduction: the problem is that we just don't know how many were procured by each means, though it seems likely that the last must have gained in importance over the centuries. If Roman slave demography resembled that of the antebellum United States more than the 18th-century Caribbean or Brazil, seizure may not have been so essential to maintaining supply. But again, we don't know, and receding opportunities for conquest may indeed have been the key factor.

But part of the answer to slavery's eventual eclipse may lie instead in the emergence of new forms of dependency, notably the status of colonus which foreshadowed elements of later European serfdom. A bound peasant responsible for his own upkeep made sense economically and in terms of the control needed to preserve order and procure agrarian labour. So the 4th century may be the turning-point, more specifically the formal application (332) of such non-slave bondage to tenants of thirty years. For the rise of the institution and its persistence (alongside modified or reduced slavery and the emergence of new peasant statuses) see vol 1 of the Cambridge economic history of Europe (2nd ed, 1966), chapters 2 and 4-6.