OK, seems I found at least a hack:
Previously, the overall feed updated date (3rd line) was always set to the publishing date of the current issue (because that is the date when the feed content last changed, right?).
<?xml version="1.0" encoding="UTF-8"?>
<feed xmlns='http://www.w3.org/2005/Atom' xmlns:news='http://itunes.apple.com/2011/Newsstand'>
<updated>2014-08-27T09:37:01Z</updated>
...
Now, I set the updated date always to the current date/time, regardless of the latest publishing date. This seems to force Apple to reload the contents and update the issue cover.