Sure sounds like a defect.
Make sure you don't have any weird settings turned on like all the equalization crap, the backlight always running, contrast all the way up, etc. Also, if you are playing extremely high quality files and picking and choosing your songs a lot--say, like, listen to one song from a playlist, then going to a totally different artist--could reduce the time you get from a charge.
Are you operating it in an extremely hot/cold environment? Have you dropped it?
None of these are probably the case, and even if they may be a contributing factor, it still may very well be a defective battery. Remember, however, that 12 hours is the ADVERTISED battery life. 12 hours is certainly attainable if you use 128k or 192k encoded mp3 files and don't change playlists too much (causing the cache to get erased and re-filled), but not necessarily a guarantee.
P.S. I dropped my 4g 20gig on the kitchen floor yesterday from counter-height. It ****ing sucked, but all seems well.