I have never seen a professionally pressed CD fail. I have seen lots of self-burned CDs fail after about three years. Of course there are archive-quality CD-Rs with projected lifespans of 100 or 300 years (if burned really slowly), but that's not what most people use for backups.
Amazon will also automatically add (most?) vinyl purchases to your Amazon Music Library, and allow download.
The Amazon downloads seem to all be 44.1 khz mp3 (just downloaded an album of mine to check).
Vinyl, with some care for environment, is really good for archival.
I've never seen a mass-produced CD (the aluminum kind) fail due to age rather than physical damage. However I have read about it happening, where the aluminum layer wasn't properly sealed in the polycarbonate and over time got corroded.