From observation of either rocks or living things, we might think that not changing is normal and needs no explanation. Rocks don't seem to change, and living things seem largely unchanged, generation after generation. This similarity is deceptive because the unchangingness of living things is a complex dynamic process that only incidentally depends on physical stability. Consider that a rock weathers away significantly after only thousands of years, while the cockroach has kept a recognizably unchanging form for 350 million years.
Evolution is necessarily a very conservative process. It is a precondition for evolution that replication be highly accurate. If a random mutation has any effect it is extremely likely to be harmful, so mutation must be rare enough that most offspring aren't impaired. Sexual reproduction makes more rapid change is possible by gene recombination, but this is still based on reliable copying of genes. Rather than being a natural consequence of physics, life's unchangingness is actually a triumph over the physical tendency for things to wear down, deteriorate and randomize.
The effort to remain unchanged begins at the level of the DNA structure that all living things share. DNA is itself redundant because it is formed out of complementary base-pairs. In addition to making reproduction simpler, this duplication this also allows DNA repair. Every living thing from bacteria up expends considerable energy in keeping its DNA from mutating.
There are two themes here:
In some sense, not changing is both unsurprising and surprising. We can understand that, due to the demands of survival, organisms have many ways of not changing, but this tendency to remain unchanged is an emergent property of life, not a direct consequence of physical stability or inertia.
We're talking about two different kinds of not changing: