Odd mini genie shutdown issue

Out of the blue, our direct tv mini genie in the family room stops and displays the no signal message. When left off overnight, it will come back on and work for 5-7 hours perfectly, and then the no signal screen comes back. Unfortunately I get the feeling this is not a widespread problem.  Here is what I have tried.  Before calling Direct Tv I triple checked all connections, re booted several times, unplugged unit and of course checked to be sure power save was not on.  Direct TV sent a new mini receiver. I connected it, it worked fine for 5 and a half hours, then the no signal message came up.  After being off overnight, it worked again in the morning, and 5 hours later, no signal.  It will not re boot, by that I mean when you hit the red button, the screen on the tv does not change to blue with the normal information. Because it has this pattern of working perfectly before not workiing, I'm not exactly sure what to try next. Has anyone experience anything like this?