I am having the same issue, the trunk would intermittently not open or close, then the battery would drain completely if the car sat for more than 24 hours. Then the intermittent part became always.... Something else that I have noticed is that the settings in the menu for the trunk (power decklid) will not let you change them.
I took the car to the dealer and they have diagnosed it as a faulty trunk control module which will set me back $600.00. I will update this post after they have replaced it...
thanks for all the information!