Looking at your watershed boundaries and points, it seems odd that there are two points in each watershed (polygon) as well as two drainage lines (blue polylines). If the points are centroids, then there is something wrong. The "two points inside each polygon" is so consistent, it makes me think that maybe you change the number of cells in the stream definition an didn't rerun some other part of the Basic Dendritic Terrain Processing functions
If the polygons are the catchment layer, then I'd check to make sure everything is correct at that step.
Flying in the blind here since I don't know everything about your project, but if you redo any step before the step you are one, you have to redo all the steps in between. There's a good chance you didn't do this, but maybe there is something is a process before the longest flow path routine that is not finishing.
I've inserted a screen capture and highlighted just the steps I use. They have to be done in order and if you re-do any step, you must redo all the following steps.
Heading out of town with limited ability to follow this. Hope you figure it out!