I have 2 LP-E6n batteries, one came with my 80D and one with the 5DIV. I never noticed anything odd with the 80D battery , I actually love it, I regularly use it in my 5DIII and it lasts longer.
However, I got into puzzling battery trouble with the 5DIV recently. I'm not sure which LP-E6n it was (maybe both?) but it happened twice that they lost a huge amount of charge while the camera was off. The last one was 2 nights ago when I went to shoot an event and the battery had been charged the day before, the 5DIV had no lens on just the cap, and when I got it out of my bag to start shooting the event, it was down to only 1 marking. Fortunately I had spare batteries with me.
Again, the LP-E6n never gave me this problem in the 80D and 5DIII.
I don't really understand the German CPS response that it's an open circuit and hence it discharges the battery. Should it be the other way?