Since there is no mention of sound, I will assume that it stays. There are three things that could be going on that it can be narrowed down to.
First thing is to make sure it is not the signal source coming in that is blanking out. If the picture alone is blanking but the TV menu (not the cable box or DVD menu) stays on then it might not be the TV. After checking the menu, try another source like a DVD player or game system. You want to make sure you have a problem with the set and not with the device hooked up to it.
If it happens on all devices then the TV might be the problem. This LCD TV uses fluorescent bulbs inside the screen to illuminate it to be seen. When they go dark, the screen becomes black. If you look very closely at it you can see that the LCD is still producing an image but there is no light to illuminate it. This can be very hard to spot. Some methods I have used to tell If the backlight is turning on or not is to dim the lights in the room and see the brightness of the screen when I have it off compared to when I turn it on at first and it still has a black screen. With the room dark enough you should be able to see light radiating from the screen when it is on. When it goes black, see if the screen goes dark like it is off. This would be the backlight turning off which can be the panel itself, or a loss of supply/on command from the boards in the set. One thing that should not change is that sound will still be present if the TV does not shut down.
If you see that the TV keeps its backlight but just loses video with all the inputs and multiple sources, then a board might be defective in the set. There are two boards in the set, the power board and the main board. The power board takes the AC and generates the DC supplies needed to work the panel and the main board. It is possible that a capacitor or a few of them have become damaged and disturb the DC supplies to the rest of the set. This would be checked with a multimeter by a technician. The other possibility is that the main board, the brains of the set, is defective and acting up. This would be more difficult to check since it could be an IC that is acting up. A technician would eliminate the other possibilities and suspect this board unless there was a telltale sign that it was the main. Also, although we eliminated the backlight from being the cause, it is still possible that the panel is acting up because there are other components to the panel that receive the video information from the main board in order to display it.
I would check the inputs first and if it is the TV then check the backlight. I think this is what is cutting out on your LCD. If the 24v supply to it is staying up and the on command (usually labeled BL-ON) then the panel is defective. A technician with a multimeter should be able to check this.