I took my Canon SD1200 IS on a snorkel trip (in a Canon underwater case) and when the glare was bright, the LCD screen did not display the scene below. Since I was holding the camera pointing mostly down, the screen would have been receiving the sun's light directly. If I tilted the camera a bit, the scene would appear. Other times, nothing would work. And at sunset, this was not a problem.
I want to know why this happens and if I can set any controls to avoid losing the picture I'm about to take. This is very frustrating when I have only seconds to 'shoot' an eagle ray or octopus and don't know where to aim the camera.
Are you sure the screen really 'shut off' and wasn't just completely swamped out by bright sunlight shining on it? Alternately, I don't know if a half-depressed button might turn the screen off (or if your controls in the housing include the "info" button that changes screen data).
If you've just shot a few pictures the screen might blank during buffering to the card...this can happen even on a DSLR as well.
If it's simply a matter of bright sunlight glare being too strong to view the LCD image then a Hood may be the answer. There are various
ones on the market, I don't know if there's any made specifically to fit your housing. A Wetpixel member posted about his DIY project to
attach a UN LCD hood magnifier to an Ikelite housing- HERE. Perhaps you could come up with a similar fix?