The behavior you are experiencing (failure to recalibrate / stuck in recalibration loop) has, in fact, been experienced numerous times by others. It is a known hardware failure mode, and if other recovery options (like the overnight bit Shane described earlier) are unsuccessful, then a replacement of the touch layer may be required.
My screen touch accuracy gradually degraded over a long period of time to the point where recalibration could not be performed and the unit was no longer usable because I couldn't press certain buttons, like you are experiencing. I finally sent my unit in, and the touch layer was replaced, and the unit is back to good as new. (During the process, I learned that I have the first 720 shipped to a customer!)
I had similar issues with my Palm V and Vx PDAs back in the day, which used the same touch screen technology. I'm afraid it's an unfortunate drawback of the technology chosen for the touch capability. It seems the tradeoff is essentially sunlight-visibility in the cockpit (the iFly's resistive screen excells here) vs. touch layer stability (capacitive touchscreens used in other tablets do not have the calibration drift issues that resistive screens do).
I now fly with both a Nexus 7 and the iFly 720. I now generally prefer the Nexus, and typically keep it on my yoke, with the 720 on the co-pilot's yoke. If I'm going to be flying for a long time with the sun coming in my window and washing out the screen, I'll swap 'em and use the 720 on my yoke.