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.
Good Luck,
ClarkEMTP