Sorry, but frankly this means that your Library of Congress archivists are either under resourced, or complete idiots. I some how doubt the latter, considering that some of the most savvy archivists I have ever met or worked with were trained there. The story is also unclear on a number of matters.
A digital recording can be reproduced without quality loss innumerable times. If they are adequately stored they will not fade. Irrespective of how you store film, or any other analogue media, it degrades. My contacts there indicate that National Geographic no longer store digital file using analogue media but do what anyone sane would do; make several copies on archival media and store them in several locations.
Magnetic digital media can corrupt easily, but most serious archives also store their material on optical and solid state media.
It is unclear from the article WHY or HOW the Duke Ellington, early sports broadcasts etc were lost, or if indeed they are gone. If they were digitally stored and were lost, the only answer is under resourcing or negligence, but they don't make it clear if they are actually gone or if they are just no longer available to the public.
The best answer to archive anything is to make digital copies on several archival media, store them properly and continue to back them up, including onto new media over time. Any analogue media, however stable, degrades over time. Ones and zeroes do not degrade. If you write them on paper, they degrade at the rate that the paper degrades, but if you copy them to new paper they will last forever. Even lost or corrupted digital data can be fixed if someone knows what the file sounded like or the image looked like; and even without that, someone can make a decent guess. Try doing that with analogue media.
I back my film photos up digitally.
Marty