Why do smaller animals survive falls from larger heights?

I can't claim to know the full answer, but it's amusing to note that this question has a fairly long history in biology. Way back in 1928, J.B.S. Haldane (my great-great uncle) wrote a popular-science article called "On being the right size", about the importance of scaling laws for biological anatomy. The following passage is relevant for the question at hand:

You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.

Haldane claimed (without offering direct evidence) that the difference could be explained because of air resistance. The force of air resistance scales as $f_r \propto L^2$, where $L$ is a characteristic linear dimension of the animal. However, the force due to gravity scales as $f_g\propto L^3$ (assuming fixed density). The ratio of these quantities scales as $$\frac{f_r}{f_g} \propto L^{-1}, $$ meaning that smaller animals are buoyed up more effectively by air resistance as they fall.

I expect that there is probably more to the story than this, however, as noted in the comments, these sorts of experiments are tricky to get funding for...

Let me try. Let's take an elastic ball (instead of an animal...) of radius $R$ and stiffness $k$, freely falling in air. The ball breakes if compressed beyond a critical fraction of its radius. Let's wait it to reach its terminal speed $v_\infty \sim \sqrt{R}$. Hitting the ground, it will be compressed by an amount $x=v_\infty\sqrt{m/k} \sim R^2$. So the compression scales quadratically with radius, and small balls have more chances to "survive" the shock than big balls.