Why do sloths come down from the trees to defecate?
From Wikipedia: 


  Sloths go to the ground to urinate and defecate about once a week, digging a hole and covering it afterwards. They go to the same spot each time and are vulnerable to predation while doing so. The reason for this risky behaviour is unknown, although some believe that it is to avoid making noise while defecating from up high that would attract predators. Consistent with this, they reportedly relieve themselves from their branches during storms in the rainy season. Another possible explanation is that the middens provide the sloths with one of their few methods of finding one another for breeding purposes, since their sense of smell is far more acute than their eyesight or hearing. It has also been pointed out that individual sloths tend to spend the bulk of their time feeding on a single "modal" tree; by burying their excreta near the trunk of that tree, they may help nourish it. [Source]