why can't I shut macbook air when cinema display is connected?

I just upgraded from an older MacBook Pro to a new MacBook Air. I have an older Cinema Display that I want to use with the new MacBook Air. I can get the Cinema Display to mirror what's on the macbook air screen, but I would like to be able to shut the MacBook Air and just use it like a desktop computer when its connected to the display (I have an apple bluetooth wireless keyboard and mouse). Every time I shut the MacBook Air it shuts down and the Cinema Display goes black. I had no problem getting it to work the way I wanted with my old MacBook Pro. Any wisdom on this? Thanks!