I have a 25A converted supply and I have to connect all of my components before turning on the PS, otherwise it shuts down as you describe.
However once everything is connected and the PS turned on, I run a Turbo 35, 2 ICE chargers and the fans of a Zero-30 all with no problems. And I charge 8k LiPo's on the ICE while charging 4200's on the CE. Never had a shut down yet as long as you don't plug something new in while the PS is on.