Index Maintenance
It's true that manually created A–Z indexes need to be updated when pages are added to or removed from the site, but so do site maps. If a web site is so large and dynamic that it's impractical to maintain a site map, it would also be impractical to create and maintain an index. For pages whose content changes frequently, such as an announcements page, an index should be written not to the specifics of the content, but merely to the general concept of announcements, so that frequent updates in the index are not needed.
If the index is created by a contracted indexer, you need to reach an agreement about how the index will be maintained. Either the indexer can be retained for future updates, or the indexer can provide written guidelines for the webmaster on how to maintain the index. For example, after writing an index for a school's web site, I identified likely additional future pages and wrote guidelines for the webmaster to indicate the entries/subentries under which such new pages would likely be indexed. In this case, the new pages tended to be individual class pages, each of which would have been best indexed in three places: under the teacher's last name, by grade level, and under the topic classroom pages.