This is actually the basis for not one but two hotly debated theses for medieval slavery: (1) Roman/Classical slavery became economically unsustainable once society shifted to systems of feudal landholding, and (2) Rules prohibiting the enslavement of Christians gradually drove up the costs of slave imports, causing slavery to disappear in Europe over the course of the middle ages. Both arguments have their flaws.

The first argument is really based on Karl Marx's idea of history—that history isn't about politics; it's rather about the deeper socio-economic changes that drive politico-ideological change. Marx argued that social relations had evolved from primitive peasant communes to ancient slave societies to medieval feudalism and on into modern capitalism. But we now acknowledge that history isn't a single one-way street but rather a vast multiplicity of stories. Ancient slavery was much more diverse than Marx thought. Since Marx was writing in the 1840s, the living model of slavery that he used as a reference was US antebellum slavery, which was a tremendous historical peculiarity for a number of reasons and forms a poor basis for understanding classical slavery. Once we start thinking about there being multiple kinds of slavery, the reasons for its disappearance must be just as diverse. New forms of landholding might help explain why the agricultural slavery of the Roman villa system disappeared, but it doesn't explain why domestic slaves went away (if, indeed, they ever really did). Conversely, domestic slavery disappeared after the US Civil War, but sharecropping and chain gangs seem to have perpetuated some of the same forms of racialized labor extraction that existed before emancipation.

The second argument is in some ways based on the opposite premise of Marx—that ideology, including religion, drives human action (rather than simply obscuring its economic motives, as Marx might more likely allege). But the fact is that few people do something just because they're Christians, and even if they point to religion as their motivation, chances are you could find a historical example of someone doing the exact opposite and still claiming that Christianity informed their motives. People's understanding of Christianity has turned them into murderers and martyrs, and it's driven both enslavement and emancipation. So in this case, I think it's possible to argue that changing conceptions of what Christianity is (and whom it should protect) gradually made slavery economically unsustainable in parts of Europe, but this is as much about the changing place of slave labor in society as it is about religion or economics.

I suspect your question was meant to target the 19th-century abolition movement, in part because there isn't much public knowledge about medieval slavery, although that's starting to change. Nevertheless, I hope these examples discourage thinking about it in terms of either economic or moral reductivism. Instead, I'd recommend thinking about it in terms of historical particularities (abolition in the UK happened very differently from emancipation in the US) and attention to how slavery—and its disappearance—must be deeply entangled in the fabric of society, from the philosophies and ethics that guide it to the economics and institutions that sustain it.

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I'm not the best person to recommend a book on US emancipation, although Sven Beckert's Empire of Cotton (2014) is a great read. For British abolitionism, I really enjoyed Christopher Leslie Brown, Moral Capital: Foundations of British Abolitionism (2006). There's also a brilliant study of Haiti: Laurent Dubois, A Colony of Citizens (1998). For the medieval period, see Jeffrey Fynn-Paul, "Empire, Monotheism and Slavery in the Greater Mediterranean Region from Antiquity to the Early Modern Era," Past and Present 205 (2009), 3–40. I'd welcome any good studies on the disappearance of slavery in the Latin world.