Batteries are not covered by warranty, except in the case of manufacturing defects.
Apple Limited Warranty:
This warranty does not apply:
(f) to consumable parts, such as batteries, unless damage has occurred due to a defect in materials or workmanship;
AppleCare Protection Plan:
b. Limitations. The Plan does not cover:
(ix) Consumable parts, such as batteries, except in respect of battery coverage under APP for iPod or unless failure has occurred due to a defect in materials and workmanship;
If it's not holding a charge because of regular use and time, it's not covered. If it dies prematurely, it might be covered.