I have switched my connection to "Bridged" and am now using the PCnet-Fast III driver, where previously I was using the Intel 1000 network driver exposed to the guest. This seems to have made things better, in that the random reboots happen much less frequent, but they still occur.
When I use the PCNet-Fast III driver on the guest and run in NAT mode, I have not experienced a random reboot. I have run for 2 weeks with no reboots, sometimes leaving the PC on overnight performing network activity to stress this area.
Thus, it seems to me that there may be some collisions or something happening in the "Bridged" mode that is causing this. My network hardware on the host is a "Broadcom NetXtreme Gigabit Ethernet" controller in my Dell Precision M6500 laptop. There may be some conflict with this driver?