Definitely a quirky issue you are having. Some food for thought...
TL;DR -
1) Switch key fobs for a while. It might be an issue with only that fob's electronics.
2) The battery costs more than anyone would expect from a regular battery. That might be why the dealer was shying away from swapping batteries.
My other car is a 2018 BMW 328d wagon. If you are not familiar with the newer BMW products, the keys actually serve as mini computers. For example, when I take it into the service department, they request that I hand them the key. Not only to give them possession of the car for the physical act of servicing it, the fob is plugged in to a module on the service writers' desk... it tells them the vitals of the car so they don't have to manually go inside of each car and record the entry data.
Finding out what kind of communication the fob has with the LC might help isolate your problem. I would assume that the LC key is a one way communicator with the car (i.e the key fob only sends, not receives info from the car) since they do not use them in a similar manner above. Either way, I would suggest putting your regular key fob where the spare is, and using the spare key only to see if it happens when a different key is introduced. That might possibly indicate whether it is solely a problem with that one key, or a much more involved problem with the key module itself. The chances, IMO, of both key fobs being defective and the key module on the vehicle not having issues would be slim.
I also contemplated saying to replace the vehicle battery (and possibly the fob battery), as
@TeCKis300 suggested. I looked up the Panasonic battery of the 200 (mostly because I've never seen a Panasonic brand car battery)... completely insane price. I hope you are sitting down when you see the price.
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