The battery life of the Ax is nothing short of amazing.
See the below thread and its link for independent testing...
http://www.aximsite.com/boards/showthread.php?s=&threadid=10070
And to add to the above, I did some test myself, running the Windows Media Player continuously with screen display toggled off until the Ax give a low battery warning (at 20%) after 18 hours!!
On several occassions, I clocked up over 10 hours of continuous use and the meter still reads 40%+
Needless to say, I am more than happy with my Ax (my last PDA only manages 3 to 4 hours before it shuts down automatically).