If the ball is rolling on the bottom try a larger ball first .
I like that!

Could be the original ball was replaced at some time.... It might work better with a larger ball.
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Chris, re. sliding contact -- If the ball is rolling on the bottom (or even sides of the lower track) the axis of rotation is horizontal -- parallel to the plane of the bed -- and perpendicular to the direction it is rolling --- just like a wheel if it had an axle. The axle is on the axis of rotation.
But when it encounters the U shaped raised sheet, the axis of rotation wants to change to vertical -- to accommodate the new edge it is riding against. Yet it is also still riding along the lower track -- so the two axes of rotation are fighting each other -- and either one turns to slip and the other remains rolling, or they both partially slip. But a ball can't roll purely in two axis at once. It can have only one axis of rotation.
Since this clock seems so sensitive to a free rolling ball, I'm guessing the friction due to slip is probably significant, where it might not be for another kind of mechanism or equipment .
Further, the slip/friction is not consistent, but happens at the turns mostly. And if the turns aren't consistent either (due to roughness of sheet metal, and the strips loosening) I imagine the timekeeping is inconsistent, and in this case it even stops.
Maybe it wasn't meant to "jump" the strips but ride on them until it hits the U turn sheet, where it rides only on that, lifting above the strips. But it would really need a fine adjustment, and the right sized ball for that.
If it rode only on the U sheet, above the track, the single axis of rotation would be satisfied.