When you have a VM clustered on multiple Hyper-V Hosts it is necessary that the machine configuration (XML) is modified to reflect the correct Switch Name on the new host during move. The Configuration file for the VM holds GUID values for "SwitchName" and "PortName". As the VM is configured with a readable Switch Name like "External" it is essential that this Switch Name exists on all participating Hyper-V hosts, and even with the same case. So upper and lower case letters need to be identical!
When you make a VM Highly Available, this Switch Name is stored in a cluster property. So whenever you make a modifcation to the VM within Hyper-V Manager, it is important to refresh this information in the cluster resource as well. Please check http://blogs.technet.com/askcore/archive/2008/08/27/cluster-resource-type-options-for-hyper-v.aspx
When this refresh is not done, you may end up with a wrong Network or even no Network for the VM after a move.