Security system

Does the security red light stays flashing even with the car off? Key out of the ignition and the door is open or if the doors are closed and unlocked? I am having trouble if I do not drive the car for two days straight the car is dead. I have had to recharge my battery several times and I am not sure what is draining the battery. Everything is off inside the car so I am baffled to why this is happening. Any suggestions please? Thanks