I have a Yamaha RX-V1500 amp and had the exact same fault. It was intermittent and would sometimes turn off straight away, or run fine for 15 minutes before turning off.
I eventually took it into a Yamaha service centre where they replaced an amplifier for the front left channel. Unfortunately they didn't provide much feedback regarding the cause of the fault. They were able to explain that the receiver turns off as a self protective measure when ever it detects an internal fault. This is backed up by the trouble shooting guide in the back of the owner's manual. All up it cost $150 and took around a week.
I haven't had any problems with the receiver since, and that was three years ago. I found the service centre by going to the Yamaha Australia website and clicking on the "service + support" tab at the top of the page.
It's better to be thought of as a fool than to speak up and remove all doubt!