One incident is a co-incidence. Two is a pattern. For the second time I dealt with a strange situation that did not seem to adhere to any predictability other than the fact that it will happen. Sometime. A Windows 2008 Server Core and now a Windows 2008 R2 Enterprise Server with Hyper-V and some virtual machines would run fine for days, then suddenly become unresponsive. The machine is up, Hyper-V VM's are inaccessible, console is locked up, can telnet to SMTP service but for the most part the system is dead. Only a hard reset helped. Until the next time.
The way I fixed the Server Core issue, and hopefully the R2 incident, is by configuring Hyper-V's network settings as follow:
Ensure the "Allow management operating system to share this network adapter" setting is OFF.
Using those settings, ensuring the Hyper-V nodes do NOT share the host LAN interface, seem to have fixed the crashing issue.