Possible Permission Issue
I know this post is fairly old, but I ran into a similar issue and my file was spelled correctly.
I originally created the app_offline.htm file in another location and then moved it to the root of my application. Because of my setup I then had a permissions issue.
The website acted as if it was not there. Creating the file within the root directory instead of moving it, fixed my problem. (Or you could just fix the permission in properties->security)
Hope it helps someone.