Hi Chris and Welcome to the VMware Community.
So let me see if I have this right... You're Windows 2003 Guest VM powers itself off. (Assuming you log into the host/vcenter with the vSphere client and you're able to see it offline..) and then the networking (vSwitch) on the host stops working? So like management access and or a vm port group for other VMs stops ?
Just trying to get more information as to whats happening.. So for starters, are there any events listed on the Guest VM events section? Select the VM and on the top bar you should see something that says events. Look in there and see what its telling you. Also, have you checked event viewer of the guest VM?
By chance do you have VMware tools installed ? If so, please make sure you're using VMXNET3 Network adapters as there are some weird issues pertaining to E1000 NICs.
Let me know what you find... Hope this helps a bit.