gee,.. I didn't think about the timezone issue...
good one.. (except I was flying west)
ok, on the return flight I tried the same thing... fully charged and "shutdown -h now"
since it was a red-eye flight, I slept instead of playing mp3s or even taking the Z out of it's case (I made my own, if you must know )
when I got home I couldn't turn it on, even with a reset and battery removal, etc...
I put it on the charger for about 10 minutes and then it did startup.
Again it showed the battery as "low" but this time it also gave me a message that the internal battery was exhausted and not to use the unit until it was fully recharged.
Now, I'm pretty sure I've left it off for 5+ hours before while remaining more or less at sea level, and still had a charge, etc. I am going to retest this tonight.
Perhaps it sat on the shelf at Amazon for too long before I bought it... either way, I think a call to Sharp is in order.
oh, and no, of course I did _not_ check it.. it was in my carry-on down at my feet the whole time