A friend owns a 2002 Saab and the battery has gone dead (twice in 5 months) without warning (even when going into the store for a couple of minutes!) As soon as you touch the jumper cables to the battery everything comes on - though the car turns over slowly due to the battery being low. Dealer checked battery and said it was strong. Car will then run normal until the next episode. Thoughts, similar experiences
There may be an intermittent internal problem with the battery. What makes me think that is your statement about the problem happening even after a few minutes of being parked. Before replacing the battery though you need to first make sure the trouble isn’t due to a bad connection to the battery or the power panel under the hood as that will cause this kind of thing also. Try cleaning the battery cable connections using a battery post cleaning brush. Hopefully that will solve this trouble.