I have noticed my battery may be starting to go.....car cranking a little slower than usual. Car usually sits for a week at a time. Anyway, I noticed that after i turn the car off and leave key in, usually the radio would stay on for like 10 minutes before shutting down.....lately its shutting down in like 60 seconds and I'm wondering if the car senses the battery getting low and is doing this to put less drain on the batt?

Thanks!