Has anyone discovered a way to shut the car off and keep the radio on?
With my TL, if I shut the engine off with the transmission still in drive then shift into park the radio remains on. This doesn't work on the 16 ILX, if you stop the engine in drive and shift into park the radio immediately shuts off.
You then have to wait until the radio boots up again.

 

The owner's manual indicates what you are doing should work, it looks like where you are failing is putting the vehicle back into Park.

Changing the Power Mode
Accessory or On Mode: Press ENGINE START/
STOP once without pressing the brake pedal for
Accessory mode. Press it again for On mode.
Starting the engine: Press and hold the brake
pedal, then press ENGINE START/STOP. Keep your
foot firmly on the brake pedal when starting the
engine.
Turning the vehicle off: Shift to or select Park, then press ENGINE START/STOP.
If you press the button and the shift lever is not in Park, the vehicle goes into
Accessory mode.

 

Yup there you go

Just leave it in N or D. It'll beep at you for a second when you do it (just to make sure you didn't do it by accident) but the car will stay in accessory mode until you shift it to P. Then it'll auto turn off.

 

Try this...

Shift to N press the start/stop button twice..Shift to park...stays in acc mode without shutting off...worked for me!

 

You could always click the start button three times to turn the engine off then accessory mode on. The radio will shut off for a minute then come back on.

 

Just press the start button once with out pressing the brake. The radio comes on