If you have a lot of connected fittings and you want to place them all again in a different point you need to place then one by one. The place fitting command should work on grouped fittings asking you to constrain just the top parent component of your selection to which the others are linked. This should work similar to copy paste inside assembly, where we get automatic constraints (connections).
Note: you can use copy / paste (no right click menu just CTRL+C and CTRL+V) and even though the fittings are connected they don't update, move to a new location once you connect parent fitting.
This is how it should work:
@dan_szymanski