....and I am not sure this really is a security issue???

One thing is to make sure all "servers" are running at the same service pack level......

When you say shut down....does it just reboot..or turn itself off

I would start disabling all 3rd party services...and see if it happens then.

Get your updates.

Look at the event log to try and determine what is happening before the shutdown occurs.

I had a bad UPS shut down my server a couple of times..was fixed by disabling that service and then replacing the UPS.