Rubber bands become brittle with age due not so much to oxidation but rather to evaporation of volatiles in the rubber/plastic material they are made of. These volatile parts of their plastic/rubber components are what keep them soft and flexible, and the loss of them causes them to become stiff and break as they age.
Keeping rubber bands in unopened or otherwise airtight packaging and then storing the package in cool locations will slow this evaporation and thus aging/brittleness. This is why rubber bands don't normally go bad in their original package but do so when stored loose after opening. You see the same behavior in the rubber (paper) pickup rollers inside laser printers which become less soft/flexible and 'sticky' to paper over time inside a printer, but stay 'fresh' for years while sealed inside their original packaging prior to installation.
I have not tested this yet, but sealing rubber bands inside an airtight freezer bag (with the air squeezed out) and then storing this in a freezer will probably slow or stop any evaporation of these volatiles if long term storage is desired. In general, colder temperatures slow or stop many chemical and physical processes, which is why freezers are good for food preservation.