ipod battery dies and then comes back to life

ipod battery dies and then comes back to life

Hello,

I have a 20GB 3rd gen ipod and I use it quite a bit. Recently the
battery has been dying after one to three hours.

I returned it to apple and they reinstalled firmware and sent it back
stating it met Apple's specification's (they did not change the
battery). yesterday at the gym it died after 2 hours (it stopped
playing and the screen said the battery was dead).

Today I was skiing and it died after 57 minutes - same scenario and
screen message. But when I returned home a couple hours later I turned
it on again (without recharging it) and it played for several hours.
What gives?

I recharge it fully (all night) and when it dies it won't turn back on.
I'm returning it to Apple again (I bought the Applecare extended
warranty) but I'm afaraid it will test normal again. Lately I've been
cross country skiing with the ipod in a backpack and running on a
treadmill w the ipod in the bottle holder - so jarring isn't an issue.
temp today about 34 F.

Has anybody else had this problem. I am a slow marathon runner and need
this thing to pplay for five hours or so.
Thanks in advance for your advice.

MOIK