To determine whether this is a battery (hardware) problem or a software problem, I'll suggest you perform a battery life test, then we'll figure out the more appropriate solution to your case.
While Lithium battery does not have memory effect, you do need to calibrate the gauge occasionally. I normally do this after 15-20 charging cycle (2 times 50% charging is count as one cycle) An inaccurate gauge can lead to the fact that the the battery capacity values are are wrong. The battery may report that it still has reasonable capacity when in fact it has a much lower value, and this causes the computer to shutdown unexpectedly. You can google the terms "Calibrate Gauge" on Lithium Battery.
To calibrate the gauge of a lithium battery, you simply need to do a full discharge followed by a full charge, so this is what I advice:
(1) turn on the LED screen to maximum brightness and set the screen to "always on", keep it running until the player turn off itself.
(2) Charge the battery overnight, till you see 99% or 100% on the meter
(3) Set the screen to minimum brightness and 30sec duration only, set it to playback on any CD quality files (Wav or FLAC) continuously til the player power off again. Keep the screen off and check the battery reading every hour, and drop down the battery readings for record.
Hopefully the duration and accuracy of battery reading will go back to an acceptable level after the calibration. If not, we'll have some data to determine if this is a hardware problem or a software problem.
Thank you for a suggestion. I will try this over the weekend.