Myron,
for TX the QMX could draw up to 1 A or a bit more. Could it be your power supply drops the voltage in this case for a very short time? This brown out may affect the controller to go to an undefined status. The display may hold the old characters but the firmware doesn't work completely from here on. Of course with the display backlight is on VCC must be available and this means the controller must send PWM to the SMPS.
Is the backlight on in the usual brightness when the QMX is frozen? Could you check the value of VCC in this state?
?
73 Ludwig