it has fallen victim to the oxygen in our atmosphere. Oxygen molecules react with the molecular bonds within the collagen structure of leather and cause microscopic cracks to form in the material. And, yes, once those cracks are formed, they will cause the material to fail much faster when it is flexed or stretched.
Hmmm...Vitamin E is recommended for dry, cracked skin and is an antioxidant. Maybe if you smeared the band with some vitamin E oil and let it sit for awhile, that would remove the oxygen from the collagen and allow it to "heal up" so that its flexibility would be restored. After the band has received this treatment, wash it off and let it dry thoroughly before seeing what the results are. IF it works, then it should flex easily. If not, then it's time to consider getting a newly minted band.
This is one of the reasons I always prefer a metal band whenever possible. They, literally, "wear like iron" because, being steel, they ARE mostly iron!
Good luck with your band...