Sounds like a power management issue with your laptop. I haven't seen this
specifically, or at least on those specs, but similar issues exist that I've
come across, but its been a while. There are a number of common problems
related to DRM, non-free chipsets, and on/off switches, but unfortunately
even when you have a laptop that in theory should work well with 100% free
software (or even just broadly defined GNU/Linux) due the chipsets they don't
always.
The first and probably near only thing to do is verify that it isn't the card
thats the problem. We can send a replacement for you to try. If it works
great. If not there probably isn't anything more to try. The updated kernel
might have been a solution (if there was a bug fix), but you've tried that
already now.
Chris