Our ponytail palm is at least 25 years old and 3-4 metres high. There are 3 "trunks" and each of these has 3 branches. The very large bulb has developed 2 splits, one of which looks as if the palm is going to fall apart. Also, in the last week or so, many of the leaves have dried and fallen off. Do we need to apply soil wetter or fertiliser to it?
If the bulb has split it could be due to overwatering.
If the plant is overwatered it can cause root rot.
Check the soil, is it wet?
I would not fertilize your plant at this time.
Allow it to dry out and see if the plant can recover.
Here is a few articles with more information.