I had an old feed for kennethreitz.com which pointed at the feed for the author’s Medium posts. If you open the repair feed dialog, paste in the new feed (e.g. http://kennethreitz.org/feed/atom/) and click the “Parse this RSS/XML Feed” button, it would eventually return a 404 – the problem being that the new feed URL was never saved and it was still checking the old URL rather than the one entered in the textbox.
The workaround is trivial: delete the old entry and add a new one.