I have many CentOS 6.6 virtual machines and each of it works just well (KVM machine, not OpenVZ container).
Well, let's check some things:
Is your VM KVM virtual machine or OpenVZ container?
How many VMs you use?
Is there are all of it shutting down?
How often your VM shutting down?
Can you specify exact time of shutting down?
Did you set "Start at boot" option on your VM?
And please make sure your host not rebooted itself.