Rubber bands are made of uncrosslinked Natural Rubber. If you stretched in a Nitogen atmosphere (and No Oxygen) the band would eventually go limp (stress relaxation , creep). In normal atmosphere it will oxidize and go brittle sooner or later as Prof Brewer points out. Any UV light around will hasten that process. read more
Most quality rubber exercise products can be expected to withstand at least 20,000 stretches under moderate use. This will decrease if rubber has prolonged exposure to sunlight, extremes of heat or cold, salt or chlorinated water. read more