I tried this workaround and it looks like it works in VS 2017. There are two versions of this workaround that my colleagues and I have tried so far:

• Manual (it works most of the time but not always): Go to Tools -> Options and make a change in text editor settings (like show/hide line numbers). Apparently that change can make the save command work again. However, there have been reports that occasionally it didn't work.
• Programmatic (it has always worked so far): I developed a VS 2017 extension with a button to save file. When the button is clicked, the code executes the command to show line numbers and then hide them. Afterward, I call the save document command. For some unknown reason, my code has worked so far for 100% of situations where normal save doesn't work while the similar manual change (described above) sometimes may not work. My save command (developed in VB) is as follows:

Private Sub BttnSaveFile_Click(sender As Object, e As System.Windows.RoutedEventArgs) Handles BttnSaveFile.Click

Try
If dte2.ActiveDocument IsNot Nothing Then
dte2.Properties("TextEditor", "AllLanguages").Item("ShowLineNumbers").Value = True
dte2.Properties("TextEditor", "AllLanguages").Item("ShowLineNumbers").Value = False
dte2.ActiveDocument.Save()
End If
Catch ex As Exception
MsgBox(ex.Message, MsgBoxStyle.OkOnly, MsgBoxTitle)
End Try

End Sub

Thank you all for your feedback!

We were able to successfully identify and fix one of the root causes of the issue and it's available in the latest 15.7 public build. We believe that issue should not be reproducible in the newer builds of VS. In case, however, if you see that the issue is still reproducing for you on the newer build, please open a new feedback ticket for the same with appropriate traces. Thank you all for your patience and feedback!

Found workaround that seems to work around the bug reliably. When visual studio stops saving the files, you just need to git commit any file (so not the file that is not being saved but any in the solution folder). As by magic you can then save the files again. It seems that there is some file watcher maybe that resets some state enabling save to work again.