I finally got around to trying these suggestions, but none worked.
To clarify: Autosave is actually working, but the status bar at the bottom of the edit screen gets stuck on "Saving draft . . . " Also, when I start a new post, the permalink box doesn't appear automatically after a few seconds until I click Save Draft. I guess it's an Ajax display issue. If I leave the page without clicking Save, the post is nevertheless saved, so Autosave works, but I don't get any feedback about it.
It's a curious but minor problem that I can live with but would like to get fixed.