My iPod mini suddenly stopped holding a charge. Is it done for, or fixable?

I can't pinpoint the loss of charge to any specific thing (I didn't drop it, for example, or damage it otherwise), but it will just not hold any charge anymore. Today, for example, it had a full charge, and in the time it took me to select an artist, a song, and fast forward a little bit, I got the "no power" message and actually watched the battery indicator roll back from full to empty in 3 seconds. Now it will turn on, and says it has 1/4 charge, but won't play and then turns off. I'll definitely take it to an Apple store, but what can I expect? Is it fixable? Or will fixing it cost me more than I spent for the mini in the first place?