I repost the index.html file and repair any broken links in the directory but later that day or the next morning the index.html vanishes again showing the directory.
Make sure the FTP syncronizes and is able to view hidden files, as well obviously switch the permissions for index.html to 755.. if not, virus or your FTP manager on the site must suck, happened to me here and there on lesser hosts.. may just be a glitch in how it mirrors..
Change your account password and see if that helps (e.g., someone has/had your password). If that doesn't help, contact your host to see if someone else is accessing your site or if something else is going on.
If you host it locally, try changing it to read-only and search your system to see if it's deleted or moved; you should also have server logs to see if/what's changed.
Rootkit. You could try to do a virus scan, and get that cleaned out of there, but you are probably so far compromised that it's probably not worth it. Reformat, reinstall, make sure your security updates are always in place.
and never, ever, have directory browsing turned on.