I have the RX - V3000 Model. It turns on for a second and immediately turns off.

I have a Yamaha 5.1 receiver. WHen it shut off suddenly after turning on, it was actually the protection circuitry kicking in (the positive end of the speaker cable to one of my front speakers had loosened and was touching the negative wire).

SOunds simplisitic, but this issue bugged me for a week before I figured out what was happening

I had the same issue and tried changing inputs and etc. within a second of time. Nothing I did worked until, I opened the lower front access door and twisted the effects knob around quickly. This stopped it from turning off and it has been functioning normally since. Even turning it off and on again is without the issue coming back. I did try most all the buttons previous to doing the effects knob, in case that makes a difference in the long-run.

Before the issue you are having started on the unit I was working on, the owner of this unit did say he was having an issue earlier with the monitor SVideo jack in back, having a role in it powering off like this, about 6 months ago. To make it work then, he would remove the SVideo cable from the monitor jack, turn on the unit and then put back the SVideo cable once the unit was on and working. This allowed it to work for several weeks to a month before turning itself off again. He would repeat this procedure and it would work fine again for awhile.
Could be an electrical or grounding issue via SVideo that messed things up more and more?

Hope this works for you too!!