When you move a duct run away, the software disconnects all the associated boundary connections. If you move a header run that is connected to an open-ended branch run, the branch run follows the header run. If the branch run does not have a free end, the software disconnects the branch from the header.
If a selection is restricted by adjacent features, use Disconnect Command to disconnect that selection, and then use Move 
to move the selection without disturbing the rest of the network.