Infiniti G25 2011, about 3 months ago I replaced the battery and my wife reprogrammed the windows so that they will automatically go all the way back up with out having to hold the window button up the entire time. A few days later we came out in the morning to all four windows being rolled all the way down. This then happened a number of different times in a number of different settings, sometimes raining sometimes not, maybe more often when raining but not sure. First we tried replacing the battery in the remote key and still happened. Then would keep the battery out of the remote key and it would still happen. After no luck I disconnected the car battery over night and then reconnected it in the morning and did not reprogram the windows and it stopped for about two months. Then today (rainy day) it happened again a number of times. Took it to the dealership and they rain a diagnostic on it and could not find anything.
To me this was/is one of the stupidest features these guys have come up with but lo, some seem to like it. I had the car parked outside while I worked on the garage door opener with the key fob in my pocket. So it started to snow and the buttons must have gotten pushed while I was working. So all four windows and sun roof open in a snow storm on a nearly new car. Stupid.
At any rate I think every time you disconnect the battery, you are losing your programming. I would for certain go back in and re-program again and leave the battery alone. If it refuses to maintain the programming, whatever the memory device is for it (body control module?) may need to be replaced. I suppose you also could have an intermittent ground or power wire disconnecting the system and putting it back in default mode again. I’d carefully study the manual to see what the defaults are, then try to get a look at a factory service manual to see what actually powers it.
Have you tried un-doing this?
I have no idea what’s causing it, but if I had that problem to aid in the diagnosis I’d want to know when the windows rolled down by themselves. Did it happen 30 minutes after you turned the key off. Or 4 hours? Or what? hmmm. you might could come with a way to figure this out without having to watch the car all night. What if you took one of those aa-cell battery operated wall clocks out to the garage, tied a string around the battery, and taped the string to the car window configured in a way so if the window went down it would pull the battery out of the clock. Then you’d know what time it happened. Another idea, I think it is possible to get a cell phone to take photos automatically every 10 minutes. How? No idea. But I recall someone here mentioning this is possible. You may never be able to solve this, but still, you’ve discovered a new hobby!! 
This is a common feature on luxury cars to have the windows open unexpectedly to let the rain in (or so it seems).
Removing the batteries from the remotes should eliminate a transmitter problem but might there be a third remote?
A couple of years ago I had a car come in with a smart key access system failing. I found a lost remote stuck between the drivers seat and console, pressure on the remote would intermittently cause it to transmit and interfere with the customers key. This customer bought the car 3 months earlier as a used car and was unaware of the extra remote.
Is there possibly a third remote lost in your car?
Double-press the unlock button on your remote, holding it down on the second press. I bet your windows roll down. It’s a feature. Keep the key somewhere the buttons won’t be pressed by other stuff in your pocket.
My car has this feature too, and I’ve never had a problem with uncommanded windows going down.
Nissan/Infiniti remote fobs are terrible in this regard. I stopped carrying mine in my pants pocket due to accidental activation, including rolling down the windows a couple of times.
Yeah. All depends on the button design. Acura was smart enough, on my version anyway, to recess the buttons into the fob housing so it’s harder to accidentally press them. I’ve seen lots that aren’t designed that way, especially in the new keyless start vehicles where the design ethic seems to be to make the fob as sleek as possible.
Those 2CV windows are beginning to look classic to me, all things considered