3 quick beeps in a series after turning car off

Does this beeping happen ONLY after you try to lock the car ?
THAT might be the result of a door lock actuator failure and is trying to tell you that the doors are NOT locked.
If one of them fails, the ALL will unlock.

The power problem likely is different and the most common cause of that it a loose main battery cable connection, usually at the OTHER end of the negative cable. Slamming the door might "fix" it too like the locking does.

Most likely two different problems, I think.

 

Nothing in the manual tied to "three beeps."

Does yours have the smart keys and pushbutton start? If so, check/replace the coin battery inside the keyfob.

 

My Gen 3 liftback uses three quick beeps to scold me if I close a door while the empty car isn't off.

 

One way I can get mine to beep after turning the key back to 'off' is if I open the door before removing the key from the lock cylinder- it's warrning me not to forget the key, of course.

Even if it had an intermittent door switch I'd think that would manifest itself elsewhere, door ajar warning or the like.

If I turn off the ignition without turning off the headlights and parking lights, I get a steady beep tone. (not sure if the tones have changed in the years between yours and ours)

 

Are there really NO corresponding little lights on the dashboard ??

Is EVERYTHING turned OFF, like headlights for instance ??

This might be solved with a 5 minute (or less) visit to a dealership.