Which model is it? When was it last serviced?
Accutrons are backwards of mechanical watches, in that you have the power source turning the escape wheel, which then powers the train up through the hands. In a mechanical watch there is an increase in speed and a reduction of torque from each gearing to the next, so there is almost no power on the escape wheel. In an Accutron the tiny power and movement of each vibration of the tuning fork is increased by 7 or 8 fold at each gear set, so that at the hour and minute hands there is tremendous power. The instantaneous date system on a 218 model will shake your wrist! And it would stop or hinder a regular mechanical watch.
The upside is a well adjusted Accutron is very reliable and runs for years and years, the downside is that they will run long after the lubrication had dried and grind the pivots to dust. I suspect the friction between the driving wheel and canon pinion has become weak, and the canon pinion and hour wheel are sticky, so the watch runs but doesn't move the hands. As the seconds pinion is before this intersection it continues to move, and the hand setting works since that is another gearing that drives the canon pinion directly.
As it does run, it should just need a service. But the longer it runs in this state the more potential damage that can be done.
About an hour and a half, but I have some helpful stuff like a toolmaker's microscope to get the position of the steady pins, screw, and point where it should sit between two teeth, a CAD program I can import an image of an original jumper, trace, and then scale a traced drawing to size, and a little CNC machine that cuts out the part. The spring section still starts at around 0.15mm and gets thinned by hand to about 0.04 or 0.05, that's where the fun is.
I understand this seems to be a common problem related to the canon. Does anyone have any advice or a link to a manual or diagram that can explain how to fix this?
the watch gums fine and when setting it the hour and minute hands move correctly.