The typical warning occurs when turning the key from position 1 to position 0 and extracting almost immediately. If there's a slight pause between the "off" position and key extraction, there tends not to be a warning beep. To reset the beep, reinsert jay, turn to position 1, back to position 0, and not so immediately you can remove your key.
It's possible it's something else. Also keep in mind that if you open the door before the key is extracted, beeping indicates to the driver exiting that the key is still in the ignition.
Let us know if your beeps are somehow different.