in the posted image there is what appears to be a remnant which could just be a orphan vertice or it could be a derrivitave vert that is linked to the mesh somewhere

if it is an orphan it should be deleted but if it is linked it could need to be welded to its parent or deleted

yes something that minor can cause the issue that you are having

another cause is that the mesh is over modded there was no need for so much geometry

what happens when you add the points is that the edges break to resemble a square

if the mesh requires that the faces be turned then you can just use the box select tools to catch the top edge verts but it the added mods are just for looks for now i would have started with a circle at 16 verts, select the circle and subdivide once, then extrude that and scale it, then grab every other vert on the top loop and scale them up or just drag them up using the grab tools

you get the same effect but it is still a single loop and easier to texture and map later