Car shifts back into N when trying to start and shift to D

Sometimes when we try to start the car, we press down on the brake, press the start button but it flashes red, not green. If we try to shift into D, it goes right back to N. We figured it was a security alarm issue, or maybe how the car was stopped, but we can't find anything in the user's manual explaining this. If we wait or keep trying eventually it works fine. Most of the time this doesn't happen, it just starts up and we're off. Any ideas?

 

Hi cwerdna, thanks for the reply. Yes, READY is clearly showing and green.