Old Lego rubber bands are known to become brittle over time and break. The two questions linked above indicate that exposure to oxygen or light is the cause, and that sealing rubber bands in an airtight bag is one solution.
In my experience it has only been rubber bands with a square cross-section that decay. I have not (yet) had one break with a round cross-section.
What other ways are there to safely keep rubber bands for long periods of time, both for storage and display?