OK, it's showing as battery failure. Contact iFixit and ask them to pretest the third battery as you have had two failures. Let them test it to see if they got a bad lot in. Reference them to this post for verification. When the new one comes in, let it fully charge then run Coconut Battery on it again and see if it is charging.
Do this a few days in a row and save the images. Report your finding back to this post and we'll see what it looks like.