I just purchased a 2007 Ls460L. I am happy to be back in a Lexus Ls. I had a ls430 when I joined this forum many years ago. The rear window sunshade keep coming up on it own when I start the car.. It will always goes down when I push the button, but It wont go up after I put it down the first time though. I searched and I found nothing about a similar problem. Just wondering If I am missing something.

 

In my car the when I leave the shade up, if I put in reverse it goes down, then after putting in Park or when driving, it goes back up where it was. In your case, maybe it is a switch at the reverse-shade-down function that could be malfunctioning? Not sure if the whole system is switch or just software based.