Usually they don't burn, but the backlight will obviously die faster (unless it's dimmed), and the display may respond a bit slower than normal if it's changed quickly after a long stint of sameness, but usually return to normal eventually.

However, tunnel vision (where the edges of the display turn dark before the darkness totally envelops the whole screen) is terminal and, so far as I know, incurable. This usually only occurs on the active-matrix models, such the PB 170 (as it did on one of mine), and the 180/180c.

I'm not sure what causes the condition. I'd guess it's a deterioration of the contacts between the display's control board and the contacts on the liquid crystal panel...