Do you promise to let us know if we give you the solution? Let us know the solution if you find it yourself in the future as well please You asked about a problem with the fob before, some five years ago, we gave you suggestions and mine was the last and we ever heard from you again. We never heard from you again about your temperature sensor question either.
I could give you a possible solution on this problem but knowing I will probably never know if it worked or not makes me hesitate to offer it.

04/28/14 was when you mentioned the temperature sensor. February 2014 is when you got the car it seems.
This forum is a treasure chest of solutions, some misinformation as well and you have to sort it out or ask for clarification.
It looks good if you try the search function rather than get people answering the same question again and again.

I do not personally need you to reply for my sake, we need results. You never reported back before.
I would be checking the CLP/SSM (pump) in the trunk under the foam behind the passenger seat for water damage. Pulling fuse #9 stops the siren but the trunk pump controls the anti theft features. The fob should cancel the alarm when operating the pump, if the pump is damaged by rain water it will not do so.

The siren batteries that leak are associated more with random alarms I think.

I'm in ft. Myers and am a dealer crossfire tech. My dealer is getting away from working on these cars and I'm picking up the slack at home on the side in my free time. I'm not sure if your car is your daily driver but if you can afford to leave it with me for a little bit I can work on it for you.