One possibility: The virtual appliance has its NIC settings cached, so when you move it from one location to another if the MAC addresses change the eth0 interface is bound to the old MAC not the new one and won't come up. We can fix it by clearing the cached MAC (support can help).
Another possibility: something's up with the NIC driver. You can try enabling a legacy adapter instead, but my concern there is that it won't work with the VLAN tagging. If it's already set to use a legacy adapter, you might let it pick up the default adapter instead.
I am pretty sure the Hyper-V NIC drivers that we shipped with support VLAN tagging, but if none of this helps resolve the issue, we might have to do some digging. We'll be updating our NIC drivers in our upcoming RC/release, too, if that turns out to be related to the issue.
The issue turned out to be related to dynamic MAC addresses during the migration. We "hard coded" a MAC address on the virtual appliance and no more issue.