Curious, what would cause any given LED display to drift or loose its stability over time.
Having investigated this in some detail, let me tell you that LEDs drift quite markedly with temperature, and to a lesser degree over time.
Monochromatic LEDs change in wavelength, amplitude and spectral shape with temperature. Phosphor based (i.e. white) LEDs vary due to the underlying monochromatic LED changes, and may have additional variation in phosphor response to compound the effect.
Over time, LEDs have a "burn in" change at the start of their lives (roughly 100 hours), and a slower change over their lifetime. The lifetime of a LED is typically quoted as the time before it reaches 50% of its initial output. Lifetime depends on how hard they are being driven, amongst other things, but are generally long, which is a good thing.
I don't have any direct experience in regard to LCD panels, but I'd be a bit surprised if there wasn't temperature and aging effects in play there as well, give the chemical/electrical nature of liquid crystal (they certainly get slower with lower temperature), and things like physical spacing changing with temperature etc. Now all this may not add up to much in day to day and less critical usage, but it is definitely there, and something to worry about if you are going to rely on a display long term.
[ If you think that making a highly stable light source is easy, then I'm sure the calibration standards people would love to hear from you! Typical light references are very expensive, and guaranteed for a quite limited number of hours. Making stable sensors has challenges as well, but seems a bit easier overall. ]