2010 Infiniti G37 Convertible

The rear passenger window goes down by itself and won't come up. This just started recently. I found three different ways to resync the windows. With the car in accessory mode, engine off, hold down the window button for 15 seconds, hold it up for 15 seconds, then hold it down again for 15 seconds. That never works. Then I read, hold the button down in the first click, not all the way down, for 3 seconds. That worked once. Then it was the same as the first method but just for 5 seconds in each position, never worked. Sometimes I can get the window up, and sometimes it stays for a while. I read that this could be the sign of a weak battery and sure enough the battery went dead, and has now been replaced. But when I went to sync the windows, none of the methods worked, but somehow repeatedly pressing the button finally got it to go up, and then I engaged the window lock button to keep it up. But now, the the passenger and driver side windows lower themselves a bit at random times. I am afraid to unlock the window in case the rear one goes down on its own again. I'm in Oregon and it is starting to be winter, so its raining a lot.  Any ideas what is going on and how to fix?