The shuttle between A and D is not always running. I am not sure of the exact hours, but I know there is an early evening period when it is not running, since that is usually when I want to use it.

Note that the train does not actually run to Terminal D. You can either use the shuttle between the D gates to the main terminal to connect to the train to A or walk to the C gates. The walk between the C gates and the train is nearly as long as the walk from C to D.