It sounds as if the Yucca is unhappy in it's growing conditions.
Full sun and dry soil are key factors.
Watering should only be when the top 3 inches of soil are dry.
Water should not hit the leaf branches.
Also good air circulation will help in plant health.
A stressed and overly watered can become diseased with fungus or insects.
Allow the plant to dry. You can apply a fungicide and treat with Neem Oil if any signs of insects.
Here are some links for you.