I think it's somewhat obvious what happened to the Knights Radiant. After they succeeded in defending the world from Odium and the Voidbringers, what would their oaths dictate they do next.....? They would then be forced to defend the people from themselves; fighting in wars and other conflicts between groups of their own people. They ended up killing their own brethren. Conflicts likely escalated or even were begun in the first place because the people assumed the Radiants would protect them. The Knights had little choice but to forswear their oaths in order to stop the senseless slaughter of their own people.< Edit: The battle that the soldiers in Dalinar's vision talked about the Knights Radiant fighting before they gave up their shards would then be one of these conflicts.> Afterward, the people hated them for not fighting for their side, which each group certainly felt was the right and just side of each conflict. After the Recreance, the losing sides of any wars no doubt blamed the Radiants for not protecting them from the eventual victors. Even the winning sides could have claimed that there would have been much less carnage had the Knights assisted them. It may even be that the whole situation was orchestrated by Odium as a way to corrupt or get rid of the Knights Radiant. Even if it wasn't a conscious decision by Odium, his influence in the world would definately have contributed to the wars that were the Knights' eventual downfall.
This is all conjecture, of course. No matter how fitting this explanation may seem, Mr. Sanderson can take any direction he chooses in the story and so until he writes it, no guesses can be correct.