Yup index.html is always required. It is probably automatically deleted because it might be changed/regenerated depending on what you do.
And yes, local playtest simply launches an integrated browser that opens up index.html, that is indeed how it operates
If the file is disappearing completely,that is definitely a problem. Try checking file permissions in your folder, see if you have free disk space etc. If that still doesn't solve it, maybe try making index.html read-only to force it to stay or something like that