Despite having a great biodiversity why is the Amazon Rainforest under risk of desertification?

The natural soil of the Amazon Rainforest is not very fertile but it is enriched by the vegetal covering made of leaves and branches that drop from the trees. Deforestation decreases this enrichment. In deforestation zones the rain falls directly on the ground causing erosion, "washing" large areas (leaching) and contributing to make the soil even less fertile. Besides that, the deforestation disallows the recycling of necessary nutrients for plants, like nitrogen. In this manner those regions and their neighboring regions undergo desertification.