"The biggest technical problem for OLEDs is the limited lifetime of the organic materials. In particular, blue OLEDs historically have had lifetimes of around 5,000 hours when used for flat-panel displays, which is lower than typical lifetimes of LCD, LED or PDP technology – each currently rated for about 60,000 hours, depending on manufacturer and model. But in 2006 experiments found that it is possible to swap the chemical component for a phosphorescent one, if the subtle differences in energy transitions are accounted for, resulting in lifetimes of up to 20,000 hours for blue PHOLEDs.[26] More recent work in 2007 by Cambridge Display[27] has extended lifetimes to 80,000 hours for blue OLEDs and for blue polymers for OLEDs, to 100,000 hours of life." -Wiki
http://en.wikipedia.org/wiki/Organic_light-emitting_diode
Ok, so apparently OLEDs now last for 20,000 hours or better.
But it is still possible for the screen to burn, so I would go with that reason as to why they are not constantly on.