Ubuntu 12.04 VM goes dead unexpectedly

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http://askubuntu.com – I'm not a super savvy super user, so I'm not sure what to look for. I have a VM running 12.04. It runs fine, and then just dies (no ping, no ssh). When I log into VMwareSphere, I see the VM still 'UP', but the console gives me a response-less black screen. This lead me to believe that Ubuntu was going into some sort of sleep/hibernate state. I double checked the power settings and found nothing out of the ordinary, so now I'm stuck on how to fix the problem. There are 5-7 (CentOS-5.8 & 6) machines running on the same server/VM setup with no problems at all. (HowTos)