At this point, seven people churp in with reports of it on AC/Home right?
The friend of mine that this happens to, has it happen on AC power.

If we assume, for the sake of argument, that domestic cats do not, in fact, spontaneously emit valid consumer IR pulse-trains, then my money is on some kind of capacitative glitching on the display board, building up very slowly but eventually causing the PIC to register an instantaneous top-button press. Perhaps if front-panel buttons were debounced a bit more it could be fixed in software?

Peter