My display, the exact (or similar/same) model as you're describing, recently displayed the *exact* same symptoms. I have a KDF-60XBR800, a 60" Sony Grand Wega II LCD RPTV, that I purchased in February of 2003. It was almost 4 years old to the day when it started turning itself off, then spontaneously powering up again after 30 seconds or so. At first it would only do it once a night or so and becoming more frequent till it was doing it every few minutes.
Anyway, long story short if it's not too late. I talked to the service tech at the dealer where I bought it. He said unplug the set, come pick up a new projector lamp/bulb (I'm not sure of the "correct" terminology?) and take it home and replace it then plug it back in. I did and the set has worked fine since I powered it back up.
Everyone told me, "it's not the projector lamp, they simply get dimmer till they go out completely". Everyone was, apparantly, wrong. At least in this case.