My battery died last year in my 2014 S3. I jump started it and drove to Audi and they said the battery had dropped a cell and they fitted a new one under warranty. I don't think you can leave the S3 switched on as it has a time out. I've sat in mine listening to the radio and an alert came on after 15 minutes or so warning me that the radio would be turning off, and the car shut itself down? If you can jump start it and drive it the alternator will charge it. If it holds a charge then yes it did run flat for some reason. If it won't charge, then the battery is defective. If its out of the car then put a battery charger on it. Put a volt meter on it and read the voltage, if it's reading zero volts then it may not recharge, but if it has 2 or more volts then it will recharge, but it may take a couple of days depending the charger. If it only charges to 10 volts then it's dropped a cell. Stand up to Audi, sounds like warranty to me.