I'm having exactly the same problem. I'll set LR to export and it might export anything from 20 up to 100 photos for me and then the PC crashes to a black screen.
I'm on Windows 7 64 bit, a hi spec machine: 8 core, 4.00Ghz AMD FX processor, 8Gb RAM. Please help Adobe! This is now officially stopping me completing jobs and getting photos back to clients!
I should note, I'm running a machine with similar specs. Windows 8.1 with an AMD FX 8350. Also stopping me from delivering images to clients.
Lightroom version: CC 2015.0.1 [ 1018573 ]
License: Creative Cloud
Operating system: Windows 8.1 Business Edition
Version: 6.3 
Application architecture: x64
System architecture: x64
Logical processor count: 8
Processor speed: 4.0 GHz
Built-in memory: 16367.2 MB
Real memory available to Lightroom: 16367.2 MB
Real memory used by Lightroom: 654.0 MB (3.9%)
Virtual memory used by Lightroom: 624.3 MB
Memory cache size: 440.8 MB
Maximum thread count used by Camera Raw: 8
Camera Raw SIMD optimization: SSE2,AVX
System DPI setting: 96 DPI
Desktop composition enabled: Yes
Displays: 1) 2560x1440
Input types: Multitouch: No, Integrated touch: No, Integrated pen: Yes, External touch: No, External pen: No, Keyboard: No
Graphics Processor Info:
Check OpenGL support: Failed
Vendor: ATI Technologies Inc.
Version: 3.3.12618 Core Profile Context 13.251.9001.1001
Renderer: AMD Radeon HD 5450
GL_MAX_COMBINED_TEXTURE_IMAGE_UNITS (actual = 32, minimum = 48)
I believe I solved my specific issue, and it wasn't lightroom. It was my PC. I ran Prime95 to stress test my CPU, and I had the exact same issue, computer shut down for no reason. Which tells me that this issue is independent of LR. It looks like the LR export was overtaxing my CPU, and shutting PC down. Possibly overheating. So, I played around with the BIOS settings and managed to get a working config... so far. I've also replaced my power supply, thinking that the old 400W one wasn't powerful enough for my new video card. For me, I think it was actually the BIOS config that fixed the issue. Hopefully that help you.