I've tried the following
- Add the site to "Trusted Sites"
- Compatability Mode
- Sign-out of all accounts in office applications
- Add FSSHTTPOff DWORD to the registry
- Open the application from IE 11, 10 and 9
- Modified Protected View Options in the trust center
These are some things I've noticed
- I am able to open it in "edit" mode once from each unique device
- I am able to open the same document in "edit" mode once using "https" and once using "http"
Things you may like to know
- The site has both forms based and windows based authentication
- The site might have had its SQL database moved between servers