The specs on those Klipsch indicate they are pretty efficient @ 8Ohms, so my first guess is you're overheating the unit. What fans are you running in your cabinet? They may not be moving enough air, or they aren't venting the hot air outside of the cabinet.
Another thing to look into, although this would typically cause a protection shutdown at most volumes, is that you don't have any strands of speaker wire crossing multiple posts or contacting the case, or crossing posts on the speaker end(s).
Have you tried listening at those volumes with the unit outside of the cabinet, just for a test? If so, and it still shuts down, you may have a bad unit that requires repair/replacement. I have an X2000 as well, inside a cabinet of sorts, that does not exhibit the problem you are mentioning (although my volume is rarely at the level you mention).
Additionally, there's a dedicated thread for the 2013 Denon line, you might want to ask there: The 'Official' 2013 Denon "E Series" / "X Series" AVR Model Owner's Thread & FAQ