Ah, now we are getting into the true "joy" of stepper repair...and why folks down on Tenth Ave often dumped them on me.
Missed counting of higher pulse counts can result from:
1) Dirty, misadjusted wallbox wafer contacts. Broken wires at the contact wafer. First, make sure the box produces the correct count.
2) Stepper springs on the clapper getting weak thus not pulling the clapper back in time for the next pulse. There is no test for this beyond holding the clapper slightly down so that it is free to move and checking ease of movement of the clapper. Problems here will typically affect only one stepper switch of the two. There are actual gram/Oz measurements but I can't find them here. Ron probably has them

3) Gummy oil or dirt on the clapper that prevents it from shifting back quickly enough to engage the stepper gear tooth. Test as above.
4) Inadequate downward overtravel of the clapper. Hold the reset magnet down and carefully press down on the clapper in question to advance it one step at a time. Closely examine how the ratchet engages the gear to hold it during the upstroke. There should be a slight amount of overtravel and back up till the ratchet dog engages. This will normally be correct from the factory, but if the stepper has been tampered with the overtravel may have been set based on the lower teeth. As this gap gets smaller due to wear as the gear position (letters or number) go higher the gap may no longer be adequate to allow the dog to catch.
5) Ratchet dogs gummy due to old or wrong oil being applied. When moved they should instantly snap back.
6) Electrical. If a tube is used it should glow purple around the cathode during conduction. Light blue indicates weak emission. This will sometimes become more pronounced during long pulse trains. I'll spare you the details as why this happens, but it is one of the reasons why a tube may work in trip but not be accurate in stepper (and why I don't use them). --Always have at least one known-good tube as spare for test.--
6a) If there is a resistor in the plate ckt (seeburg steppers) check it for accuracy. These take a big hit due to the pulsed nature of conduction. Wirewound won't have this problem but I prefer to use a carbon ½ w so as to act as a fuse and protect the coils. Every year or so I replace that resistor as they do change in value in this service.
7) If there is a capacitor in the plate ckt as with Seeburg, it -must- be accurate. In a 5mfd, going just one mfd higher or lower causes miscounting about 10% of the time. I have long used mylar caps in this service and even after 20+ years of heavy service they are still as rated.
I have previously mentioned the backlash problem due to gear wear. typically this causes the wiper contact to touch two rivets at once, but depending on how the wafer is positioned a minute shift can cause it to contact only the lower rivet. When reassembling I connect continuity tester to the center terminal and while holding down the reset (butterfly) I advance the stepper wheel one notch and look to good contact at only the correct contact. At certain positions of travel a visual is possible too.
The rest magnet hold capacitor should keep the magnet energized till write-in is completed and scan starts.
As always, make sure everything is moving freely and not dirty.
I know this sounds like a lot to check and do, but most of these are one-time. I have steppers in commercial service for well over 20 years (oldest since Oct 1989) and other than cleaning the wafer rivets every 5-7 years and occasional contact point checks actual problems are rare. In home use you'll probably never revisit any of this once done right.
Rob