Update: Video - Canon 6D turns itself off after a few shots with fully charged battery

Question

Update: I uploaded my video to youtube, please comment:
http://youtu.be/3PNLUYd8g7A
TIA and pardon me for my English.
I posted this originally at another forum, and somebody suggested me to post it here as well, to get more help.
Long story short, I purchased a brand new Canon 6D from B&H on Oct 24th, 2013. From early december, the camera starts to shut itself off randomly and displaying empty battery. I found the camera constantly shuts itself off after 20 - 100 continuous shots with a FULLY charged battery (right off charger, showing 8.23V using multimeter, and showing 98% in battery info).
The camera will just turn itself off in the middle of shooting, showing empty battery int the shoulder window. The solution is simple, open the battery door, then close it again, no need even to pull the battery.
So, I contacted Canon support, sent the camera to the VA service facility, waiting for it be repaired. As an engineer myself, I understand things fail, and I thought this is such an easy issue to reproduce, anybody should be able to repro it.
Couple of days later, I received a phone call to send my accessories in, no problem, debugging needs more info, that's normal. I sent my lens and stuff in. I unfortunately had to bear the cruel fact that I don't have a decent camera for the holiday, though I have a backup.
After a long wait, on 12/28the, the accessories were delivered at 9:35am. At 10am, they called me, they were sending the camera back. No issue at all. I was like, have you tested AT ALL? They didn't care, sending the camera back regardless. 
I received the camera on Jan 2nd, and saw the same issue on that day. Of course, it was NOT fixed at all.
I googled really hard, somebody said he had similar issue but it was a defective battery, so I got a brand new Canon battery, unfortunately, the same issue pops up again.
Ok, the only choice for me is to send it back again.  But this time I am totally amazed by Canon.
I sent the camera in again with my lens and battery. Also, a video showing the issue on a standalone CF card (I know 6D does not take CF, just to put the video on it).
Couples of days later, they called asking for accessories, I was like, what accessories, I don't have any more.
Then the camera sit in their facility for a few days for nothing. All of sudden I received a phone call on Monday morning, said it is ready. The camera has no issue at all.
I called, asked whether they have watched the video, they told me two technicians, including a senior one, was not able to upload the video to the computer. I was like, what the hell? why the heck you need to upload it to the computer, find a card reader, plug the card in, double click, how simple is that?
I talked to the service manager over the phone, he told me that there is nothing he could do, if their technician said so. They have decided to send my camera back, NOT fixed, again. I esclated the issue again, but haven't heard anything back yet.
Honestly, I am totally pissed, how stupid can they be? I included a letter with detailed steps on how to reproduce this issue. As an engineer myself, I know how easy to reproduce this issue. But what shocked me is that they don't even know or they didn't even bother to watch the video. In the same letter, I asked/begged them to contact me if they cannot reproduce the issue instead of just sending it back unfixed.
Guys, any other ways to get their attention? I already filed a BBB complaint. For a brand new camera of 3 months old, it has been in Canon's repair shop for almost a month. Leave to say that I missed the most importand holiday season in the year. This is simply not acceptable.

Answer 1

"The camera usually shuts itself off after 20-100 continuous shot, ..."
By this you mean your are in continuous drive? You just hold the shutter release down until it stops shooting?
"... the shoulder LCD shows a ..."
What is the "shoulder" LCD?
Sorry for the extra questions but I am trying to understand exactly what you are going through and why Canon said it is OK.
Canon did not say it was all right if it is not.
You are, also saying, if you use the camera, just for a single snap shot, say several in a session, it is OK? Right?
It only shuts down when on continuous drive or video?
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