A statement from a Quora answer which still holds even thought it's quite an old one,

I enjoy saving articles for offline use, for instance when flying. One thing that is not entirely clear to me is how you can update an article to its most recent version; presumably, simply by saving again, but the interface doesn't make it too clear how this works.

Currently the most straight forward way to fix this is to show the new "Downloading 1 article" notification when the app updates an article present in the reading list. The app is said to update the article in a reading list whenever a user visits it whilst online.

Initially recorded at T184827#3912844