What Causes the Droop Down of Corners of Mouth?

This a natural part of the aging process related to chronic exposure to gravity and muscle movement. You cannot avoid these unless you have no facial expressions and live in a gravity free zone. Genetics, exposure to extreme climates and smoking can accelerate the process so these should be avoided.

My response to your question/post does not represent formal medical advice or constitute a doctor patient relationship. You need to consult with i.e. personally see a board certified plastic surgeon in order to receive a formal evaluation and develop a doctor patient relationship.

Sagging of the corners of the mouth is a natural part of aging. A facelift usually is not enough. Fillers alone improve but, are not perfect. Botox of the depresser muscles will help but, this is tricky.

As one ages, the soft tissues around the mouth descend.  Often this can be improved with a facelift and/or facial fillers.