There are a lot of settings inside your material.
The first thing that I would change is the Material> Render> Clip Strokes To Screen. If unchecked, this will help to calculate the whole object, instead of the visible part based on the screen visibility.
The core idea is that the scene is seen as a 2D world. It doesn’t create the strokes in 3D. Which means that lines that get interrupted during grow by camera moves, will perhaps be evaluated as gone.
Some settings, like Filter Strokes, can by them self do more harm than support, while a camera animation is changing the situation constantly.
Anyway, some drawing options might run into the problem that a stroke vanishes, as it is 2D after all for S&T
Here is your scene file back
A quick preview
Next, set your color for the second material to a different one so you can exclude one or the other if something doesn’t work correctly.
The lines are based on the settings of the material, and a very thin line (one pixel in your example) and a dependency of others, like depth or opacity, might influence the result.
Cineversity has a lot of tutorials about it, and I certainly encourage you to check them out. Sketch and Toons has a learning curve, and I can’t take that learning curve away with a single post here. When S7T was released, it was a complete module with its own manual. Those borders have vanished, but nevertheless, it is a mighty package and needs some attention.
I would start with Kai’s exploration of the Line types. Perhaps some presentations from NAB or Siggraph, and of course the series about it, some are older some are quite recent.
If a problem occurs, I suggest to go step by step, and after each line is established (error free), go to the next. Of course, to just check all options and see what happens is tempting, and you can go from there. Taking a few features off, see if it stable or not and exclude or include others. I can’t fix the settings that you have done without knowing any prioritization of the targets, there might be something that eliminates each other.