The most likely reasons for the display going funny over time that I can think of are:1. Display overheating. Is it getting warm? Are you quite certain that there really is a built-in series resistor for the backlight, and the way you are connecting the backlight does not bypass it?2. Supply voltage dropping, possibly because the voltage regulator that is powering it is overheating and going into thermal limiting mode. Put a meter across the 5v supply and see whether you get a steady 5v.
What happens if you don't connect the backlight? The display should still be readable in good light.