Most likely because your battery has seen near its limit of charge cycles and is due for replacement. It is no longer capable of holding enough charge to power your laptop for more than a few minutes. Replacing the battery should allow your computer to hold charge for 5 or 6 hours like new.
MacBook Battery is the battery for the Macbook you listed, but be sure your computer is the one pictured on this page or it may not be compatible.
Apple Original OEM Battery. Replace your dying or broken battery with this OEM replacement. Compatible with all 13.3" MacBooks (excluding MacBook Unibody and MacBook Air). 4900-5200 mAh, 55 Watt Hours (Wh). White and black options available. — 20 available at 99.95 each.