I think I may have resolved it. It continued to turn it self on and off randomly after updating iCue and Firmware, so I started looking at it as a mechanical issue.
I pressed the button to turn on recording and then pressed it again and held it down as far as it would go, below the bezel and held it there firmly for about a couple of minutes. I wanted to see if it would come on while I had it pressed. After a couple of minutes I released it and it hasn't come on since. I tested turning it on and off, and it still work.
Just one of those weird issues.