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Final update: after changing the battery of the key fob, it did not have any apparent effect at the first. BUT, after the 1st day, it started to work really well again. After 10 days' experience, I am pretty confident that changing battery solved the issue. So it is not due to a defective car battery IN THIS CASE. If my car battery dies in the next 6 months, I shall report back. Otherwise, consider the mystery is solved. Thanks for the help!
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