iOS mail .ics files won't open in Mail app

Whenever I try to open a calendar appointment (.ics) file sent via email, I get the image to “Tap to Download.” When I tap it, it flashes “Downloading” for a second then back to “Tap to Download” and nothing happens.

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It works fine on Mac, but I prefer to do a lot of work on iPad. This suggestion from discussions.apple.com didn’t work.