After thoughts on this before sending back to CW towers for a repair.
C1 Moonglow V1.
Date doesn't change at 12, whether from manually winding the hour hand past 12 and/or waiting for the hour hand to pass by 12 of its own accord.
Pulling out the crown and winding the crown successfully moves the date marker.
Would one expect the date wheel to fail to move when the crown is pulled out if the main date feature isn't updating when the watch is left to run?
I'm guessing there's a gear wheel disconnected from the main gear chain and the date wheel?