Try replacing the little, silver memory battery. My local grocery store has them for $1.50. It's worth a try.
While that silver memory batt is out, also remove the main (rechargeable BP511A) batt(s), and then press the shutter release button exactly once. This will "reboot" the camera. Put the batteries back in. You should need to reset the time and date after doing this. Probably your custom functions will need resetting, too. Rebooting the camera completely like this might clear some bad instructions "stuck" in the camera's circuitry.... might or might not help... but it's free and easy to try.
If you have extra BP511A, have you tried it (or them, since it sounds as if you have a grip that uses a pair of batteries)? This would eliminate the possibility that the batteries are at fault.
Do the batteries work in your 30D after a charge? This would eliminate the possibility that your charger(s) aren't working right, would tell you if the batteries are getting fully charged.
Is the rechargeable battery(ies) run down after the camera dies? I.e., does it take a full charge? If so, it sounds as if the camera is draining the batteries very quickly, which would indicate something wrong with the camera that's causing it to draw far, far more power than usual. I can get 1000+ shots with a pair of freshly charged batteries in 50D/BG-E2n.
If the batteries aren't drained, check the battery contacts on the batteries and inside the battery grip, and remove the grip to check the contacts on it and up inside the battery. Inspect them with a flashlight and clean the contacts with a tissue moistened with isopropyl alcohol (rubbing alcohol).
You also might try using the camera without the BG-E2n... Just with the single main battery inside the camera. This might tell you is the fault is with the grip.
If none of the above helps, I'm afraid the camera will need to go to Canon service. Being that it's a year old with only 9000 clicks, any repair might be done under warranty. Canon will let you know.