If you are using a version of draw.io and saving fails, for whatever reason, you can obtain the XML of the diagram and manually save it.
In the menu select Extras->Edit Diagram, select the text that starts and end with <mxGraphModel> tags, open a text editor, paste the XML in as a new file and save it. That file will be loadable back into draw.io using a fresh browser tab with www.draw.io loaded, opening the file from the local device where you saved it.
Note that the XML is only the XML for the current page. If you have multiple pages, you need to switch to each page and save the XML separately.