Following an informative and helpful discussion with Adonit support about the disc lifespan and warranty, I decided to write this small post so that other clients and prospective buyers would be able to easily find this information.
Disc lifespan It seems the discs should last 4-6 months of normal use and having one break at that point in time is not covered by the 1 year warranty on your stylus. Discs are considered to be consumable parts, just like your printer's cartridge. If you are buying a jot stylus from outside the US it would be wise to buy some replacement discs as well to avoid high shipping costs down the line.
Disc warranty With the exception of "dead-on-arrival" and manufacturing defects there is no other stated warranty for these discs. The Adonit 1 year warranty does not apply to discs.