I've been having this problem since updating to iOS 9. It happened on my old 6 Plus, and now it's still happening on my 6S Plus.
Basically, when my phone is in portrait mode, it won't switch to Landscape mode unless I moved to a different page on my homescreen...it will then flip to Landscape, but then will be stuck on that. Same thing with switching back to Portrait mode...I have to physically touch the screen to move to a different page for it to move back to Landscape.
Never had this happen until iOS 9. And no, it has nothing to do with Orientation Lock being turned on.....
I've also had an intermittent problem with two folders on my home screen (bottom left 2) being distorted. I'll restart the phone and they'll be fine, but then will randomly revert back to looking like this.
