Premature sleep when on battery--why?


When operating on battery, my 15" Powerbook (10.3.9--2 years old)) used to auto-sleep when battery strength was very low -- say 2%-3%. Now it does so, and must be plugged in to awaken-- when battery strength meter says 55%-60%. After awakening the meter says 0%. Also, battery seems to be draining much faster.

New battery?....or what? Why does the meter still read a high level of charge before sleeping?