The human apolipoprotein E gene (ApoE) has several alleles segregating in the human population. One of them, E4, is associated with increased risk of Alzheimer's. Ed Yong, writing for The Atlantic, asks "Why Do Humans Still Have a Gene That Increases the Risk of Alzheimer's?I can think of several answers off the top of my head. The most important one is that Alzheimer's has very little effect on your ability to have children. The disease may not even have developed in most of our ancestors who tended to die younger. In order to be subject to negative selection the allele has to affect adults before they reproduce.
The second reason is that the slight deleterious effect, if there is one from an evolution perspective, may not have been significant enough in small populations. I know, and I hope my students know, that neutral and deleterious alleles can reach significant frequency in a population by chance. The general public doesn't know this.
Check out Ed Yong's article to see his explanation.
“It doesn’t make sense,” says Ben Trumble, from Arizona State University. “You’d have thought that natural selection would have weeded out ApoE4 a long time ago. The fact that we have it at all is a little bizarre.”