My C720 shuts down as well.  Someone in this thread suggested that it was related to whether or not the adapter is connected:

https://productforums.google.com/forum/#!topic/chromebook-central/gjSnZJeMEls%5B1-25-false%5D

I've yet to have it shut down when the adapter is connected, whether or not the adapter is plugged into the wall.  Although that's not an optimal solution, it has removed a lot of the frustration to have a workaround.

Thanks,
Myles

On Mon, Feb 9, 2015 at 7:20 AM, Aaron Durbin <adurbin@chromium.org> wrote:
On Mon, Feb 9, 2015 at 1:32 AM, Matthias Apitz <guru@unixarea.de> wrote:
> El día Sunday, February 08, 2015 a las 11:14:10PM +0100, Idwer Vollering escribió:
>
>> ?
>>
>> 2015-02-08 21:55 GMT+01:00 Matthias Apitz <guru@unixarea.de>:
>> > El día Sunday, February 08, 2015 a las 02:40:45PM -0600, Alex G. escribió:
>> >
>> >> Suspect number one is the device overheating. The shutdown is
>> >> triggered by the EC. I don't know how you can enable ACPI debug output
>> >> on BSD though. On linux, it would be "echo 1 >
>> >> /sys/module/acpi/parameters/aml_debug_output", so whatever the FreeBSD
>> >> equivalent of that is.
>>
>> hw.acpi.verbose=1 would be a start.
>> ...
>
> Thanks for all the hints.
>
> As I said, the events are sporadic, seldom, but complete power-off (like
> as you would cut the cable from the motherboard). Of course the system has no
> chance to write anything to /var/log/messages or console.
>
> My hope while writing to coreboot@ was to get a pointer to the list of
> open ore solved issues within coreboot and/or SeaBIOS to see if this
> issue is somewhat known, solved or could be related to some known or
> solved issue. Where can I find such a list which is normally (as we do
> in my company) attached to the Release Notes of a new version of
> software.
>

On the surface this doesn't sound like anything coreboot or SeaBIOS
specific. Can you grab the cbmem console logs on the boot after the
power off (cbmem -c)? There is also an eventlog sitting in memory as
well that can be grabbed.  mosys
(https://chromium.googlesource.com/chromiumos%2Fplatform%2Fmosys/+/refs%2Fheads%2Fmaster)
should be able to do that work for you: mosys eventlog list

The last thing to get is the EC console log. That's much harder to get
as you have a kernel that doesn't have the EC driver in it. If you
feel adventurous the tool (util/ectool) can be found here:
https://chromium.googlesource.com/chromiumos%2Fplatform%2Fec/+/refs%2Fheads%2Fmaster

Hope that helps.

-Aaron