The reason your edge loops aren't continuing as you would like is because you've created n-poles towards the end of your crescent. You've done this in order to maintain all-quad topology, but all-quad topology is only useful as long as it lets you continue edge loops as you want to. The corner where the three highlighted lines intersect, as far as the topology is concerned, is exactly identical to the corner of a cube. Blender doesn't know which edge to continue the edge loop down, so it stops there.
Option 1: Take the Triangle
In this case, you can just leave triangles there. They're not really going to screw up a subdivision surface modifier, and for the most part they will let you continue to add edge loops along the geometry as needed.
Option 2: Better Quad Geometry
If you really want to keep to quads though, you simply need to add some more geometry which puts your quads in the right places.
This arrangement preserves quads, but doesn't put those inconvenient poles along the edge loops you want to select: