Interesting, I had an Emotiva MPS-1 amp that kept shutting down when driving my 80's at no so loud levels, at least loud my my definition for monoblock amps to shut down. I ended up sending my amp back to Lonnie at Emotiva.
I don't think the RPA-1 has the same limiter switch my MPS-1 had, so it may not be the same problem. Is your amp sitting on a well ventilated shelf, or is there no ventilation. Do you have other equipment right above it, or are you allowing for air movement.
If memory recalls, you need at least 4 or more inches around/below/above the unit so it won't overheat. What is behind the equipment, is it open or in a closet with no air flow?