I agree with Rich, it should go out after 15 mins. My P2 does the same thing and goes out after 15 mins of power shutoff, I believe that is the standard with Tekonsha controllers.
Yes, I think 15 min is correct if the trailer is not connected. (You are being warned that you're not "hooked up" - red screen.) If the trailer is connected, it will always be on if the ignition is on and the readout will be green.