This has also been happening since December. Figured it was time to contribute officially.

It's gotten to the point that I don't want to sign up for Duty Finder or Party Finder anymore and EX Primals are out of the question because this issue could easily cause a wipe. This issue is killing my ability to play the game.

There is not common point at which this happens and has happened at every possible point:
After hours of play (solo in cites, in the field, in a party in an instance, etc.)
After less than an hour of play
At the start screen before I could even connect to a data center

Details using official PC Template:

Time: Random
Frequency: 1 to Many Times a day
World name: Exodus
Character name: Briareos Donoho
Class/Level: BRD 50
Party or solo: Both
Steps:
1. Play Game
2. At some random point Screen Goes Black and must reboot
3. Repeat

Connection Specs
- Type of internet connection/provider: TWC 50Mbs/5Mbs

PC Specs
-=-=-=-=-=-=- System Information -=-=-=-=-=-=-

SYSTEM_OS Windows 7 Ultimate 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.130828-1532)
SYSTEM_CPU Intel(R) Core(TM) i7-2860QM CPU @ 2.50GHz (8 CPUs), ~2.5GHz
SYSTEM_CORE_NUM SYSTEM_CORE_LOGIC 8 SYSTEM_CORE_PHYSICS 4
SYSTEM_BIOS InsydeH2O Version 1.0 A05
SYSTEM_LANGUAGE English (Regional Setting: English)
SYSTEM_MEMORY 16365.824MB
SYSTEM_VIRTUAL_MEMORY 2047.875MB
SYSTEM_PAGE_FILE 32729.828MB
SYSTEM_STORAGE C:\ SYSTEM_HARDDISK_DRIVE SYSTEM_TOTALDISC_SPACE 228.699GB SYSTEM_FREEDISC_SPACE 12.767GB
SYSTEM_DIRECTX_VERSION DirectX 11
SYSTEM_GRAPHICS NVIDIA GeForce GTX 580M
SYSTEM_GRAPHICS_DEVICE \\.\DISPLAY1
SYSTEM_GRAPHICS_CHIP NVxx
SYSTEM_GRAPHICS_MAKER NVIDIA
SYSTEM_GRAPHICS_VRAM 1998.438 MB
SYSTEM_GRAPHICS_SHARED_VRAM 2048.309 MB
SYSTEM_GRAPHICS_DAC Integrated RAMDAC
SYSTEM_GRAPHICS_DISPLAY_MODE 1920 x 1080 (32 bit) (60Hz)
SYSTEM_GRAPHICS_DRIVER nvd3dumx.dll,nvwgf2umx.dll,nvwgf2umx.dll,nvd3dum,nvwgf2um,nvwgf2um
SYSTEM_GRAPHICS_DRIVER_VERSION 9.18.0013.3221
SYSTEM_GRAPHICS_DRIVER_DATE 12/19/2013 3:33:31 PM
SYSTEM_GRAPHICS_DRIVER_LANGUAGE English
3.0
SYSTEM_GRAPHICS_PIXEL_SHADER 3.0
SYSTEM_GRAPHICS_VERTEX_TEXTURE SYSTEM_SUPPORT
SYSTEM_GRAPHICS NVIDIA GeForce GTX 580M
SYSTEM_GRAPHICS_DEVICE \\.\DISPLAY2
SYSTEM_GRAPHICS_CHIP NVxx
SYSTEM_GRAPHICS_MAKER NVIDIA
SYSTEM_GRAPHICS_VRAM 1998.438 MB
SYSTEM_GRAPHICS_SHARED_VRAM 2048.309 MB
SYSTEM_GRAPHICS_DAC Integrated RAMDAC
SYSTEM_GRAPHICS_DISPLAY_MODE 1920 x 1080 (32 bit) (60Hz)
SYSTEM_GRAPHICS_DRIVER nvd3dumx.dll,nvwgf2umx.dll,nvwgf2umx.dll,nvd3dum,nvwgf2um,nvwgf2um
SYSTEM_GRAPHICS_DRIVER_VERSION 9.18.0013.3221
SYSTEM_GRAPHICS_DRIVER_DATE 12/19/2013 3:33:31 PM
SYSTEM_GRAPHICS_DRIVER_LANGUAGE English
3.0
SYSTEM_GRAPHICS_PIXEL_SHADER 3.0
SYSTEM_GRAPHICS_VERTEX_TEXTURE SYSTEM_SUPPORT
SYSTEM_SOUND Speakers / Headphones (IDT High Definition Audio CODEC)
SYSTEM_SOUND_DEVICE_ID {1540DEC6-E064-4B5F-BAF6-222FE311CA81}
SYSTEM_SOUND_DEVICE_NAME stwrt64.sys
SYSTEM_SOUND_DRIVER_VERSION 6.10.6320.0000
SYSTEM_SOUND_DRIVER_LANGUAGE English
SYSTEM_SOUND_DRIVER_DATE 3/21/2011 11:48:16 AM
SYSTEM_SOUND SAMSUNG-1 (NVIDIA High Definition Audio)
SYSTEM_SOUND_DEVICE_ID {0DA11DDA-2AA5-479A-84A9-1A076A45A5BB}
SYSTEM_SOUND_DEVICE_NAME nvhda64v.sys
SYSTEM_SOUND_DRIVER_VERSION 1.03.0030.0001
SYSTEM_SOUND_DRIVER_LANGUAGE English
SYSTEM_SOUND_DRIVER_DATE 11/28/2013 8:38:18 AM
SYSTEM_SOUND Speakers (2- Logitech G930 Headset)
SYSTEM_SOUND_DEVICE_ID {271372C9-2674-49AF-9392-D7E259EF7E97}
SYSTEM_SOUND_DEVICE_NAME USBAUDIO.sys
SYSTEM_SOUND_DRIVER_VERSION 6.01.7601.18208
SYSTEM_SOUND_DRIVER_LANGUAGE English
SYSTEM_SOUND_DRIVER_DATE 7/12/2013 5:40:58 AM
SYSTEM_SOUND Communications Headphones (IDT High Definition Audio CODEC)
SYSTEM_SOUND_DEVICE_ID {3C3AF891-C32B-4582-BD80-61C91C9009DF}
SYSTEM_SOUND_DEVICE_NAME stwrt64.sys
SYSTEM_SOUND_DRIVER_VERSION 6.10.6320.0000
SYSTEM_SOUND_DRIVER_LANGUAGE English
SYSTEM_SOUND_DRIVER_DATE 3/21/2011 11:48:16 AM
SYSTEM_SOUND Digital Audio (S/PDIF) (IDT High Definition Audio CODEC)
SYSTEM_SOUND_DEVICE_ID {FA65BF85-C74D-444D-87FC-801D6DD7C037}
SYSTEM_SOUND_DEVICE_NAME stwrt64.sys
SYSTEM_SOUND_DRIVER_VERSION 6.10.6320.0000
SYSTEM_SOUND_DRIVER_LANGUAGE English
SYSTEM_SOUND_DRIVER_DATE 3/21/2011 11:48:16 AM
SYSTEM_INPUT {6F1D2B60-D5A0-11CF-BFC7444553540000}
SYSTEM_INPUT_NAME Mouse
SYSTEM_INPUT_REMARKS SYSTEM_GAMEPAD_AXIS 3 SYSTEM_GAMEPAD_BUTTON 8 SYSTEM_GAMEPAD_FOV 0
SYSTEM_INPUT {6F1D2B61-D5A0-11CF-BFC7444553540000}
SYSTEM_INPUT_NAME Keyboard
SYSTEM_INPUT_REMARKS SYSTEM_GAMEPAD_AXIS 0 SYSTEM_GAMEPAD_BUTTON 128 SYSTEM_GAMEPAD_FOV 0
SYSTEM_INPUT {5DFD5C20-4BB3-11E1-8001444553540000}
SYSTEM_INPUT_NAME Controller (XBOX 360 For Windows)
SYSTEM_INPUT_REMARKS SYSTEM_GAMEPAD_AXIS 5 SYSTEM_GAMEPAD_BUTTON 10 SYSTEM_GAMEPAD_FOV 1
SYSTEM_INPUT {7617B1A0-6102-11E3-8001444553540000}
SYSTEM_INPUT_NAME Audio Controls
SYSTEM_INPUT_REMARKS SYSTEM_GAMEPAD_AXIS 0 SYSTEM_GAMEPAD_BUTTON 5 SYSTEM_GAMEPAD_FOV 0

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Laptop Model Name: Alienware M18xR1