I have LG and played dual play Black Ops 2.(sold it a while back now)
So you enabled it in game settings and TV settings too? And it just switches back by itself? Dunno what that could be,sorry.
Just a note,try dual play without enabling it in the game setting,just TV,its a little stretched but does work.Does it switch back then too?
For eg Ghosts doesnt have dual play setting but I tried anyway just by TV setting,on PS3 again,its a little stretched and res is cut down ofcourse so looks a little flat,not the best,Blops 2 must compensate somehow for this with its dual play setting I think.
However Ghosts on PS4 works better with dual play setting on TV enabled,its still stretched a little,but cause of the better graphics power it still looks good and is perfectly playable.I must say though that even in split screen graphics are good,albeit split across the middle.
Its just to bad that Ghosts doesnt have an ingame dual play setting.
Note to all: Any 'passive 3D' TV can dual play,you just need the dual play glasses,which are just 3D glasses but with 2 left lens's and the other has 2 rights. This is how it works,so it hides the image from the other player,it does work well overall,you can sometimes see some ghosting from the other player,usually if the background is dark,however its a great alternative to split screen.
Again,works best if the game also has dual play settings in its graphic setting otherwise it looks a little stretched.