Ive tried putting it on airplane mode as well. No luck, my battery will only last 5-6 hours playback. If I leave it without turning it off it will discharge in a couple of days.
Before you go to the trouble of changing out the battery or getting a new DAP, I would suggest charging the ZX1 up to 100%, and then allow it to play back until Android itself performs its "emergency" automatic power off.
If you want to accomplish this relatively quickly, I would suggest turning the screen to max brightness, set it up to never turn off, and loop play a video file of some sort (and leave wifi and bluetooth on, for that matter).
You MAY just be dealing with an issue of Android being confused about how much battery capacity the battery actually has. So it may be showing you that it's down to 10%, when if fact, it has much, much more.
Performing the above steps can "realign" the graphical representation of the battery capacity with the actual battery capacity that remains.