First, the alarm siren has it's own rechargeable battery...so it will work (for a while) even if the vehicles battery is dead. It will eventually die if it is not being recharged by the vehicles battery.

Second, have you unlocked your instrument cluster so that you can perform OBC TEST #9 (which will reveal the battery's voltage with the engine NOT running and ignition in position 1)? Or do you have a multi-meter so that you can check your battery's voltage to make sure that its voltage isn't dropping low? A battery voltage of 11.89 volts means that the battery is at 0% state of charge. Which means that there could be some reserve capacity in the battery to operate some light-weight electronics.

Low vehicle battery voltage will also cause the DWA's alarm siren to sound off...when the central locking system is activated when the car's battery voltage is low...the DWA alarm can interpret this as a thief trying to disconnect battery power...thus it sounds off.

Double check the health of your vehicle's battery with some type of testing equipment that will provide voltage numbers so that you can truly dismiss it as the culprit.

And if your instrument cluster is displaying the BATTERY charge warning light...that would indicate that the alternator is not keeping the battery charged...so take another look at the alternator if this is the case.

Good luck.