Grasshopper auto-saving only works when you have saved the document at least once. This widget save each new document to keep the auto save always active and avoid losing the not saved work. Automatically saves new documents in the GH AutoSave folder with a default name.
It has a small and unpleasant problem, it forces you to use "Save As..." to give another name and location. And well, it increases the amount of useless files in the auto-saving folder. But at least you'll have the reassurance of not losing your work when Rhino/GH crashes.
This is something I had done for myself but I decided to share it because it's been working well for me. If you don't like it or it didn't work, shut up or improve it, here is the code in C# from VS: Github repository.
Default name format: unnamed (day.month.year, hour.minute.second).
You can turn it on or off from the widget tab: Display > Canvas Widgets > AutoSave Plus.
GH AutoSave folder: File > Special Folders > AutoSave Folder.
To install: copy and paste the AutoSavePlus.gha in File > Special Folders > Components Folder, and restart Rhino+GH.