I have one with the same problem. I just drilled a couple of holes either side of the ON/OFF switch and screwed a piece of rectangular plastic across the switch to hold it in the ON position. I just turn the monitor ON and OFF at the mains now :-)
EDIT - Just looked at your photo. My 1084S has the ON/OFF switch at the rear. Yours looks a bit older model with the ON/OFF switch at the front, and might be tricky to bodge in the same way :-D