-   I have the same problem. Watching T.V. with my grandkids and the T.V. just keeps turning off by it self. Now it won't stay on!!!!-   sstraughn
I had the same problem with my Son's TV ( Disney Cars 13" TV/DVD). It would work for a few minutes and then turn off. After reading the other posts, I found one that mentioned dry solders in the flyback section. I removed the back cover, again pretty easy with the help of another post on this site. (remove the lug nuts, and then the 6 screws that hold the wheels on. With the wheels off you can remove the 1 screw per side that need to come off. In addition, ther are 2 small screws by the video out section, and the 2 more screws at the top of the back secton.) really not bad.
I labeled each of the cables, and then removed the main board.
I used a basic soldering iron and retouched each point on the power and flyback sections of the board. I did not really see anything that looked bad, but I'm technician but I have played with electronics over the years.
reassembled and it works, it has been on for an hour now.