If it just turns off by itself, you might have a problem with the power supply. But, if it turns on and off by itself, it could be some kind of overheating problem in the power control circuit.
Or it could be something more bizarre. I have the following suggestions (I used to teach cable TV repair and we actually had this kind of problem).
First, check to see if there isn't an extra remote under a sofa cushion or something. We had a situation once where the customer's TV kept changing channels by itself. Turns out the customer's remote had slipped under the sofa cushions and, whenever she sat down, it would push the channel change button. We figured it out by using a video camera. They're very sensitive to the infrared light from the remote and it showed up as a very bright red dot whenever the button got pushed.
Or, maybe someone is using a similar remote to yours and it's coming in from a window. When we would walk around the cable company building and the customer service reps had their TVs on particular channels, we would walk by across the room with remotes and change their channels on them. Maybe somebody is messing with you by pointing a similar remote through your window.