I will give you the facts as I see them and hope that you can help regarding the health of my yucca plant - please see picture:
1) approx 2 years in this pot and prior to about 1 month ago leaves were always upright and a lovely healthy green colour.
2) I have watered the plant once each month with a good soak and the compost drains very well and soon the compost is only a bit damp and probably for most of the month the compost is fairly dry.
3) The plant stands in a place where it gets direct sunlight only in the later part of the afternoon although its situation is quite light and bright.
4) The site is centrally heated
As I say this problem has just arisen about a month ago after about 2 years of healthy life and I am not aware of any changes that have occurred
Outside United States
I would suspect a fungal infection or insect infestation.
Have a look in the bottom leaves and stem for any insects or dead tissue. Cut out any dead tissue. Yucca have buds on the stem, so if the roots are healthy, you could remove the damaged shoots and wait for it to re-grow.
Also look at the roots, if there are a lot of black/brown roots the plant will struggle to survive but Yucca are quite resilient.
Let us know what you find so we know if to recommend a fungicide or insecticide.