I would suspect that this issue is inside the HVAC ATC control head itself. These ATC modules are addressable with the DRB III scan tool and can store fault codes. It could be fractured internal solder joints or pin terminal connections.
Like the digital instrument clusters and radio displays, electrolytic capacitor life and the VF display tube power supply DC-DC converters could be failing.
You could open it for a look and good used ones are out there if you need one. Discussion here: http://www.lhforums.net/forums/showthread.php?19187-Concorde-Heater-Control-display-problems