It's something I've wondered, too. I know that the time of year a trauma or difficult event occurred can cause psychological suffering when it comes around again, but a physical recurrence of pain upon the actual anniversary date? I don't think I've heard of this. In the "real" world, some wounds still ache anyway after "healing" ... perhaps they might
psychosomatically do so on a significant date, as well as on others?
Perhaps it was Tolkien's invention, since at one point it was to be the place of the wounding that proved the trigger, not the date, but he changed this. (I think that's in one of the HOME books about the development of the story of the LOTR). Since the Morgul-wound was supernatural/demonic in nature, it wouldn't have to be governed by real world science/psychology.
One thing that does connect to actual experiences reported by soldiers, though, is the continuance of pain in a severed limb - the arm or leg still hurts even though it is no longer there. Again in the early drafts, Frodo said he felt pain in the finger that had gone, at the same time as the shoulder-pain returned, but this did not survive in the final draft. Maybe Tolkien made a conscious choice to connect the physical suffering to the chosen laws of the weapons/supernatural injuries he had subcreated, rather than to wounds in the "real" world?
It slightly puzzles me why the bite of Shelob would continue to cause trouble ... I suppose it's to do with the darkness of Ungoliant (who poisoned or at least devoured the Two Trees), of whom Shelob is the last child, and the fact that not many people who suffered a bite from Shelob lived long enough afterwards to become case studies or provide comparison/estimated prognoses for the condition.
I really must read the copy of "Tolkien And The First World War" that I purchased so many years ago. Not that I''ll necessarily get an answer there ... but I want to read it anyway.
Perhaps there are literary precedents? Was Arthur's wound of this nature?