Silly question - are you winding it with the crown (don't worry about "over-winding") or are you simply picking it up and shaking it to wind it with the automatic (presumably bumper) mechanism? Could be that it's just running out of power?
With the crown pushed in / normal position, just wind it about 30 times for a full wind (it won't stop due to the automatic mechanism). Next day, do the same, and so on. If it still stops, then it probably needs a service.
If the hands turn freely when you set the time, then they're not getting caught on each other, I'm not sure what else would make it stop suddenly when still keeping good time.
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