First off, let me admit: I suck at electrical problems! My nearly new (2 months old) battery doesn't seem to be charging off my alternator. I can jump start it with cables and it runs great. Turn it off and the battery appears to be completely dead: lights don't turn on, won't turn over, etc. Had anyone seen this before? Is there a fusible link or relay I should look at?
Firstly look if your terminals are properly tight. That usually causes bad charging before looking at the electrics.
Maybe check your charging system? A $10 multimeter will give you the reading. Check at idle and at 5000 rpm (ballpark) Should be in the 13.5 range, but you can find the exact spec online or in the handbook Edit: my learned friend above made a wise suggestion too. I usually assume that's been checked because loose terminals tend to show up when you attach jumper cables, but it still needs to be verified
Pull the battery and have it tested at your local major chain auto parts store. Should still be under warranty.