If you’ve administer a web site, try not to link directly to the index page but rather its directory. Specifically, you want to link to yourdomain.com/directory/ rather than yourdomain.com/directory/index.html.
I just recently modified an index page on my web site from an html to a php suffix. Fortunately, I had all the links on the web page pointed to the directory rather than the file itself so I just renamed the html version of the index file to something else. No broken links.