I like vinyl. But as a backup medium CDs are just as good if not more robust, I think. I have yet to experience a single CD failing. Even CD-Rs turned out to be pretty robust unless being handled with an utter lack of care.
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.
I have a pressed CD that failed. It is a regular audio CD from 1993 or 1994, and it developed tiny black flecks all over the aluminium foil. I guess it is not perfectly sealed. I think I still have it somewhere, even if I just bought a replacement for some € during a sale... so yeah, it can happen, after a small amount of years.
Wrong on the CD-Rs: I've seen them fail before, due simply to age. It happens with the cheap ones; the "archival quality" ones really do seem to be much better, but I have some ~15 year old cheapies that are dead. You can even see on the disc that the dye has changed colors and is uneven.
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.
