it might just be old age

another possibility is that it might be competing for sun and water with the japanese maple. rhodies like morning sun and shade in the hot of the afternoon.

The new vegetation seems to be very healthy, so it could only be old and grow slow

After 58 years you should be able to write a book on the issue. I would say its just old. I'm new to rottos but I never heard of deadheading them.

It is just old and excessively leggy from reaching for more light. You can cut back hard (I would wait until spring) but regrowth will be slow and of course no flowers for several seasons. But both the amount of shade and its advanced age will have an impact on how well it will do going forward but a well-sited, healthy rhody can live many decades.

Deadheading is usually done for aesthetic reasons, removing the unsightly spent bloomstalks and preventing unnecessary seed development. Whether or not it aids in flower set in following years is up for debate - no one ever deadheads wild rhodies and they seem to do just fine without. FWIW, the very old (60+ y.o.) rhodies my garden are simply far too large to deadhead and they bloom profusely each season.

yea my rottos and azaleas, and lilacs for that matter do great without deadeading.

When a rhododendron truss is removed shortly after blooming, new growth begins to grow much sooner than if the truss was left on. That new growth has a much better chance of forming a bud for next year's bloom.