It might help to understand how those sketchy line styles work. when you select a sketchy style, raster images of the drawn line style are laid over the edges in the model. For example, the Conte Crayon style found in the Sketchy Edges style uses the images shown here.
The shortest line image is 32 pixels long. If an edges is shorter than 32 pixels on screen, it’ll not be shown. There are other settings that affect that, too.
It’s common to see curves disappear when the edges are exploded. Welding them can help as can enabling Profiles.
Too a point. The shortest edge length available for the sketchy edges styles is 16 pixels.If that is used when making a style, it’ll help to retain the detail. If settings like Halo are not set in the style, that’ll help, as well. Welding edges on curves goes a long way, too. For that, the best tool is Eneroth’s Auto Weld. Compare the center front leg to the others. I exploded the curves on the center leg.
Sometimes you can manage by changing the face style to a shaded one. It won’t make the edges show up but it can make the shape appear.
Custom sketchy styles can be made quite easily but it requires Style Builder which is part of the Pro package. Your profile indicates you are using the free web version. Style edits are possible on the desktop client versions but not currently on the free web version. Auto Weld is an extension which the free web version can’t utilize either at this time.