You might want to consider contacting an administrator to get this thread moved over to the Pioneer forum, you might get more responses.
As for your problem, the relay is clicking off because of something going wrong. Sounds obvious right? If the unit works for long periods at low volume, maybe it has a high DC offset? I'm not sure how this would work, but if the offset is high, turning up the volume might amplify this until the protection circuit activates. The high DC offset doesn't always have to come from the power amp, there could be something going on in the pre-amp section as well. I had a Sansui AU-D11 mk2 that had a high DC offset (among other things), and that was coming from the pre-amp.
Another cause could be the amp is getting too hot when the volume is higher, and shutting off because of that.
Get this thread moved over to the Pioneer forum, and I'm sure you'll get more advice. Oh, and download a service manual.
Lee.