Split from this thread.
I have the exact same issue with Excel 2016 (build 16.0.8326.2096), and it happens even with files that are stored on OneDrive (a OneDrive for Business account, but using the new unified sync client).
I am sure it is not an issue of where the file is stored, because when I open the same workbooks on a different computer using the same version of Excel, I do get an active auto-save toggle, and am able to turn it on and auto-save successfully.
Also, auto-save works in PowerPoint 2016 with files in the exact same directories.
I cannot find any reason why auto-save should not be working on that one computer. They are using the same version of Excel and the same version of the OneDrive sync client. The only difference is that the computer where auto-save does not work in Excel,
runs Windows 7, while the one where it does work runs Windows 10. No relevant-looking differences in settings, as far as I can tell, but I would appreciate it if you have suggestions for settings that I should check, including using regedit if necessary.