Let’s see if we can figure this out from first principles. Limiting ourselves to biological evolution, evolution needs a few things to work in practice:-
–a mechanism of inheritance. Genes in our case. Consider stones. Stones don’t have genes. Stones don’t evolve (biologically, that is. I know a pebble back in my village river that somehow manages to accumulate little pebbles around it that are more smooth. I think it’s cheating.)
–one or more heritable characteristics. For instance, Lactose tolerance. Our ancestors couldn’t stomach milk–until about 30,000 years ago. Lactose tolerance evolved, multiple times in various groups. Most of us can now digest milk because we have inherited the necessary genes from our ancestors. Some of us have’t inherited the gene and suffer from indigestion when milk (lactose, to be precise) gets in.
–selection pressures. For instance, marginally better survival of babies with milk tolerance (this is presumably how we evolved lactose tolerance)
Take away one of these pre-conditions and biological evolution will hit a wall. So, it appears to me that evolution could stop if one of the above conditions is not met.
Digression: Here’s an idea for a science fiction story. Imagine a civilization that has deliberately and methodically removed all the above evolutionary pre-conditions, in other words, hey presto, an Utopia! All the saints and philosophers of this Utopia have committed sepukku (cut-me-tummy, japanese style)–saints, because they understood gods were not needed to attain perfection; philosophers, because they lost their vocation. The inheritors who remain face a conundrum. They are perfect, and they are absolutely miserable. Who shall rock the boat and release their kind from the irony of it all…