Well, first off, remember what leprosy is and how it works: a deadening of sensation. Bits don't drop off because they randomly fall off, but because you don't notice how damaged they are. This could well lead to ornate wrapping/unwrapping procedures, where the leopards carefully cover themselves so as to avoid any kind of injury, but also uncover themselves to check for wounds or infections. Being in the desert is actually to their advantage, here, since the more arid conditions will severely reduce the chance of fungal infections.
This also plays into the harshness of the desert conditions, since sandstorms or other gritty winds could strip flesh. So venturing out of the safety of the shelter is even more dangerous for the leper leopards than for others--so only the most skilled or foolhardy know the way through the desert.