While modeling, the face center of certain faces got misaligned. It disables loop cut through all the faces that were selected. All the faces are rectangles. You can view it here:
I tried to reset by selecting all faces and Mesh> Normals> Reset Vectors
Also tried using Shift + N to Recalculate Outside. The face center of two faces are not in alignment with the neighboring faces.
Even turned on Face Orientation to check whether faces have any issues. 
Kindly suggest a way to re-align the face center with neighboring faces, so that loop cut can be done seamlessly.