ESX will not shut down a VM when high memory usage. There are several memory reclamation mechanisms that will kick in.
When it happens you should check the hostd and vmkernel logs on the host as well as the vmware.log / vmware-x.log in the VM folder on the datastore.
Otherwise it could be something going on in the guest but then...
If you wanted the VM to power on when it's off you'll have to use PowerCLI and run a script as a scheduled task on a server for example.
something like:
if ( (Get-VM "CentOS-VM").powerstate -eq 'poweredoff' ) { Get-VM "CentOS-VM" | Start-VM }
If you decide to go that route, remember to disable the task when you do some maintenance on the server.