Why can't sloths survive outside the tropical rainforests of South and Central America?

Enough said. :) Why can't they? Predators or does the rainforest provide a certain type of leaf they need to eat?

No safe places to hang out here.

i think its not their habitat

They can survive outside the tropical rainforest, you can find them in zoos across American (see citation below).

If you meant in nature, there are many reasons. Mainly their low and unstable body temperature is very sensitive to climate and light. Also the rainforest provides the blue-green algae which grows in their fur to help camoflage and protect the slow-moving/defenseless animal.