I have the exact same thing happening to me. Every night the screen pops on and I cant keep it off. I powered it down last night to get it to shut down. I tried a hard reset today to see if maybe something got screwed up some how. Also i turned off led notifications for my wordfued app thought maybe linked some how so will see tonight if that helped. Though it doesnt seem there are many people having this issue as your post is all I can find for it.
Update: called customer care this evening they said it was not a known issue and shipped me a replacement so i guess we'll see. I will update if those things fixed it or not. And i know there is no led for the app to turn on but thought it may cause a issue having it checked. who knows.