Natural selection only pushes towards the removal of things that harm reproduction, not things that harm survival at all ages. If appendicitis mostly happens after the average age of reproduction, then there's not really a big evolutionary pressure to remove the appendix. Sure the person will die of appendicitis, but if at that point they've already had all the kids they're likely to have during their life, then the appendicitis doesn't have an effect on the process of natural selection.