The driver side on my 2008 did the same thing. I popped off the "leather" covered round plug on the side to access the bolt inside. Tightening the bolt fixed the problem and now the armrest stays level.
Mine was a broken weld on the seat frame holding the bolt mount from kids sitting or falling on it while climbing to the back. I had to peel the leather off of seat back and drilled and bolted it as I couldn't weld it.