Not to be contrary, but I disagree with the assertion that continuous heat in the LCD is what leads to eventual failure. Rather, it is my assertion that heat cycling contributes to premature failure, as it does in any electronic device. Repeated expansion and contraction of components is the culprit. That includes all of the semiconductors, passive parts, and the switching power supply. I keep mine on all the time with a UPS and the added benefit is when you are ready to work, it sounds the same from 10 seconds in as it does hours later.
I'm not saying you should keep yours on, it does waste a lot of electricity, but the fact that electronics are wounded by thermal expansion and contraction is not unique to our consoles or audio gear in general.
Best,