As the Japanese maple grows, the rhododendron receives less and less light so growth is confined to those areas that receive some direct sun or at least more intense light. Rhododendrons also vary in how long they retain individual leaves. Some hold on to them for only a single year, others up to three years. Fertilizing yearly is probably unnecessary unless a soil test indicates a need. In any case, fertilizer will not encourage growth in areas that are too shady to support it. From the evidence of the photo, your rhododendron looks perfectly healthy. It is just adapting to the changing conditions of its environment. Japanese maples are usually good companions for rhododendrons so if your neighbor would agree to limbing up and/or thinning the maple's canopy, the rhododendron would likely eventually respond with growth lower down rather than just at the ends of the stems.

Thank you for your thorough reply. I have asked my neighbor to thin the maple, but it was a very incomplete job and that was about 4 years ago. They are great neighbors and I don't know if I want to ask them again as they, in general, do not believe in pruning!!!