That is a normal characteristic for lithium polymer batteries… they deliver to the end and then just die. Sort of like a total cardiac arrest.
Most battery types go through a gradual charge decline and provide some warning of their demise.
Rechargeable lithium polymer batteries are the same way… sudden death. Lithium ion are more user friendly, as are zinc/carbon, lead/acid, alkaline, NiCd, NiMH and several others.