The thing to note here is that pulling the lever out pushes the assembly toward the cannon pinion. These are really then just two gears whose teeth must engage in order to work. It is possible for the gears to happen to come together in a position such that they do not line up and engage.
If this happens, which is really just a matter of chance, a slight turn of the crown will move the wheels a little so the mechanism can engage.
This next photo gives a better view of the other side of the cannon pinion. There is a tooth missing, and at least two others are badly bend over to one side. This is a result of the gears being pushed together with force when they are not aligned.
Even under good conditions, the way these wheels come together makes the teeth on these brass gears subject to wear causing an uneven and rough feel to setting.
This is an old Elgin design (the model is similar to the first watch Elgin ever made in fact). But it represents the highest state of the art for this technology and manufacturing for its day. It's over 100 years old. The design is not like a modern watch would be, and it is far from perfect. Even just slightly later watches have a completely different clutch design, improved to better avoid such problems.
Parts for these watches are becoming more and more scarce. In the not so distant future it will become vastly more difficult to repair a problem like this.
Let's be careful with these old machines.