Hi 

I've just come back to playing endless space again after hearing the second one is in development and everything was going fine until I encountered another race and went to open the diplomacy screen, upon doing so the display stuttered and froze before recovering then stuttering and freezing again until it blue screened itself. I had a look at the output file which is included below and there was an entry which seemed relevant

Skipped rendering frame because GfxDevice is in invalid state (device lost)

(Filename:  Line: 1385)

HandleD3DDeviceLost
  HandleD3DDeviceLost: needs reset, doing it
FullResetD3DDevice
ResetD3DDevice
dev->Reset
D3Dwindow device not lost anymore

output_log.txt

AUTOSAVE 1002.bin

it basically repeated this error until it blue screened or I Alt-Ctrl-Del out of the application which did not respond after doing so

My Specs are 

Intel (R) Core (TM) i7-2630QM CPU @ 2.00 Ghz

8.00 GB Ram

Windows 7 64-Bit Service Pack 1

NVidia GeForce GT 550M

sorry can't really get you a screen shot as its basically a black screen as it fails or a blue screen that doesn't let you screen shot

Game version is Disharmony 1.1.58

I hope this helps to find a solution

I've been having the same problems too. When clicking on the diplomacy tab on the main screen it consistently freezes and I have to force quit (on MacOS). :(