I'd love to re-read all the Pern books, but unfortunately, I don't own any of them. A friend of mine had sent them to me, years ago, and I had to send them back when I was finished reading them. Hmmmm, maybe I can start collecting them in eBook format. Hmmmm . . . .
She was a good writer and I got about 8 or so of the Pern books but I'm an extremely logical and analytical person and that closed time loop in the first trilogy buggs me. Badly. Lessa has to go back in time to get the Old Timers because she went back in time to get them because she went back in time to get them etc. There is no possible in universe initiating agent that I can see. The only way that I can see to initiate the loop is a Whoiverse type situation:
Universe 1 has something very bad happen in the past that wipes out the other dragon riders and a lot more. The Lessa from there come up with the idea of going back in time to try to rescue the riders but doesn't have time/means to do the same for all the other people that would be affected. What she actually does is go back in time and sideways into a parallel universe.
Universe 2 Lessa comes up with the idea of going back in time to get the riders and ends up going into universe 3 and comes up with the idea to leave a message for herself.
The story we have is the universe 3 result of that.
That's fine for Dr. Who but buggs the heck out of me in other story worlds.
So, is there a story world with a closed time loop that doesn't bug me? Yup. Babylon 5.
When the loop first appeared it annoyed me. But when I decided to see if I could reverse engineer an in universe starting point/ initiating agent I actually succeeded. What I ended up with is the series we see as being timeline 5 time loop iteration 4. I spoke of this to my husband and a few months later he found comment online that made it clear that I was basically correct. I'd missed at least one detail though. The reason the Grey Council had three of the devices that Delenn used to metamorphose was because of the three previous iterations of the loop.
ETA: Yes, Myth. I'm well aware that British slang has a completely different meaning.
My husband spent a couple of years in England as a young teen.