Hi i would suggest it is an overheating problem, with no image they show a blue screen, they run much cooler with this (thats why its blue) if you put an image on and it then shuts down it may be overheating try opening the menu see if it does the same, or display a blue image from your computer see if it stays up?
What is the lamp age (in hrs) is it possible either have ever been turned off with out cooling first?
Marc