I have never edited a document and then tried to put it back in DocuWare, but this is an example of doing it in .NET:
Are you using .NET or straight HTTP calls? What version of DocuWare? Cloud or on-premise?
One thing I notice is that editing operations involves downloading the content of a document (as "Sections"), which appears to be different from downloading the whole document. It is also an asynchronous process.
I am not sure what the .NET calls translate to in terms of the URLs to use... Looking at Fiddler as I edit a document, it looks like one of the relevant resources is:
Like I said, Sections vs Documents -- not totally sure what the difference is, though.