Same problem here. I can charge it in a regular wall outlet, but the car charger drains it more, if anything. Like others have said, recent updates seem to have made the battery drain faster so now I need to be able to recharge during the day. Found these instructions for the HTC One, but didn't fix the DNA:
1. Turn phone OFF
2. Let charge for AT LEAST 10mins even if it doesn't look like it's charging (mine DID show the new charging animation)
3. Press and hold POWER + VOL UP + VOL DOWN for AT LEAST 2mins. Anything less will not reset the charge mode.
4. After 2mins release the buttons and the phone should boot as normal.