Some of this discussion may be relevant:
Short version is that a coplanar face need not be surrounded by coplanar edges. I think some of the connected faces are not quite coplanar, and at one point in your featured triangle there are multiple line endings that are almost in the same location. Drawing a line away from there will only connect to one of the line endings. Drawing a line that ends there will connect to all of the nearby line endpoints, and have the effect of creating one face per line ending that isn’t quite identical to the other ones.
In that discussion sWilliams made an extension, that lets you make a set of selected edges and faces really be coplanar. I tried the extension on your model, and it seems to make things work, without having to flatten the geometry onto the ground.
Here is that extension, it appears as Flatten to Calculated Plane, in the Extensions menu.