If you are using an intelligent DC-DC power supply like an M2-ATX, that unit requires constant power to be applied to the accessory line to initiate a startup. When it detects a loss of power to the accessory line, it commands a shutdown.
Some units have a boot lockout feature so that once it detects power, it won't check again until some number of seconds later. This is to allow the computer to boot completely before shutting down. It keeps voltage cutouts on the accessory line (like when you turn the key to start the car) from causing a shutdown.