It's a power supply related problem. When it turns itself off, this it called protection mode. The TV automatically turns off to protect other parts form being damaged.
The most common problem is the Power Supply Unit or the Backlight Inverter Board.
You may have to take the TV to a repair shop to find out which one is bad. Paying a repair shop to replace the board for you maybe more than the TV is worth. If you let them
diagnose it and you replace the bad
circuit board yourself, it would be cheaper.
Here's a place I use to get parts for TVs:
http://www.shopjimmy.com/catalogsearch/result/index/?q=LC-26D43U&p=1
The problem is the repair shop may charge you double or three times of what the part costs at the web site link above. Then, plus labor. I just want to save you money. :)