"Elastic", of course, is simply rubber encased in some kind of fabric. Like everything else made of rubber, it doesn't last. Both natural and synthetic rubbers dry out, crack, out-gas their plasticizers, and otherwise age. Try stretching a 5-year old rubber band and it'll break. I just threw out a bag of rubber bands from 2001 as only 1 in 10 still worked.
Use the door pockets as intended; the elastic is going to age anyway. While I wouldn't overstuff them so the rubber is under tension at all times, I wouldn't avoid using them either. I keep the owner's manual and a map or two in them; mine are approaching 6 years old now (replaced of course during the restoration) but still work fine.
Michael Salemi
1969 280SL
Signal Red w/Black Leather
Restored