Why did Frodo feel he had to leave Middle Earth at the of ROTK?

[Inziladun]

Originally Posted by Pervinca Took

But is to sail West to sail out of Time, or have I misinterpreted the meaning of passing out of Time? (Since I seem to remember a Letter mentioning that the healing of Aman was still "within Time"?) What I mean is: would there even be an October the 6th or a 13th of March in Tol Eressea or Valinor? Would he be protected from these bouts of illness by being outside Time? I know that elvish settlements even in Middle-earth have a timeless aura to them, but they still used calendars, I believe? What is the case beyond the Sea? Are there still seasons and years? * And if not, would this alone prevent the return of illnesses triggered by a date?

A very interesting question. My take on it is that since Frodo in Eressëa would not be "outside" time to the point that he would become immortal like the Elves, ie his body still would be subject to physical death, he would also potentially have still been afflicted by his past wounds. Tolkien seems, in the quote, to have left the question with ambiguity. Maybe the Undying Lands would have provided Frodo spiritual healing without question, but the physical effects were more permanent.