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Is your car a 2004-06? If so, The SMART key can stay in your pocket to unlock doors, start the car etc. If this key is in close proximity to your car when it is in the house for instance it is constantly communicating with the car. This draws down the battery.
To stop this communicating press the button under the drivers side dash to stop the key from communicating when the car is being left for long periods. ( see next post for location) I also hook up a trickle charger to the battery. I don’t drive my car when the weather is bad or for trips to market. When you do drive your LS if your RPMs don’t get over 2000 I don’t think your battery is charging. So on short trips your car is is being started and not charging the battery. Also, do a search in this forum on battery issues.
Hope this info helps.
I did get the picture from the manual however that was the wrong one. Here is the correct illustration. Page 34 of Keys section. 2004 issue.
the rest of my comment I received from other members posts on “ dead battery” issues.