Coefficient of restitution of a ball question

[Jeven]

Why is the coefficient of restitution of a ball independent of the height it is dropped from?

A mathematical explanation would be best. Thank you.

 

[nasu]

I suppose is just an approximation, for deformations within some limits.
Besides, for heights larger than some limit, the ball reaches terminal speed in free fall and the collision speed does not change after that.
But some context will help.