Oh, the pessimism!!
As you will be able to tell, I am new to this site and am currently really enjoying my time here. I don't think there's any worry that interest will wane.
Like many Tolkien nuts, I'm absolutely confident that despite the movies having all been released, interest will remain the same. Why? Because it shouldn't be forgotten that the movies can in no way overtake the pre-eminence of the books. There are always new angles to explore, new perspectives to think about, deeper appreciation when reading the books to enjoy etc etc.
The books will always stand the test of time - movies come and go. Plus, age shows up more glaringly in cinema. In 10-15 years will we look back at LoTR and find that it looks out-dated? The same questiion won't be asked of the books, i'm sure.