Hi, i have a similar if not identical problem. Have a kdf-e50a12u in the spare room, it's also abt 6/7 years old (rear projection bravia). It stays on for about 5-15 mins each time it's turned on, but turns itself off into standby mode, where the normally red light is, it blinks between green and red. If the tv is turned off at the button and on again, it restarts as normal and lasts a further few mins.
To repeat it is the standby light which flashes green/red.