This question has been asked many times before, and the advice is that the chronograph mechanism should be left running to minimise wear. The same applies to the Seiko 6138 and 6139 vintage chronographs. This advice relates to the design of the mechanism and the use of a ‘vertical clutch’ – I understand that running the chronograph locks the clutch in position so there is no slippage. However, I’m obliged to Adrian Licu who has provided more information via his comments on the Automatic Chronographs page after he did some research on this issue. Although the advice to run the chronograph stands, it is also recommended that the watch is sometimes run with the chronograph stopped in order to avoid the clutch parts seizing together. Here is the key part of the information Adrian kindly included in his comments. This advice was given about the Seiko chronographs, by Al Archer a Canadian watch maker:
‘……when the chronograph is turned off, the two parts of the chronograph runner have friction between them, since the large wheel must turn for the movement to run, and the chronograph hand does not move. Running the chronograph eliminates the friction between those 2 parts, but adds other loads such as the friction between the 2 ends of the shaft that the chronograph hand is attached to (one end in a jewel, the other in the tube of the center wheel). Also, there is the added load of the minute counter ticking over. Not sure I would say off or on has the most load – I would have to have the watch on the timing machine and measure the balance amplitude in both cases to confirm if one has more load (and lower balance amplitude) than the other.
But one thing you need to do with these is to run them with the chronograph off at least every so often. This will help prevent the chronograph runner parts from seizing together.’
I’ve amended the Chronographs page to include this advice.