There are a few dramatic conventions which snap me out of media instantly, but none (or nearly none) as completely and annoyingly as this bit of fluff. A quick, short, and complete example is in the first Matrix movie.
Oracle: “Don’t mind the vase.”
Neo: *turns* “What va-”
Neo: *disturbs vase by turning, which falls and shatters*
Oracle: “That vase.”
Neo: “How did you know?”
Oracle: “Ohh, what’s really going to bake your noodle later on is, would you still have broken it if I hadn’t said anything?”
A stable time loop is a series of events in which the future alters the past to ensure that the future event happens. Complicated and clever stable time loops appear to add complexity to a story, and can end up being fulfilled in a dramatically interesting and unexpected way, but I can never think about them for more than a few seconds without the framework of the story dissolving, and revealing the bones of the time loop; It Was Written In The Script.
Now, obviously this is true of everything in every scripted media. But the point of the media is to make you forget that fact. Media sets up chains of causality, claiming that effects flow from causes. The Bad Guys attack the Hero’s house, so the Hero jumps out the window. The Hero hurts his ankle jumping out the window, so he seeks medical aid and meets the Cute Female Lead at the hospital. The Cute Female Lead doesn’t believe the Hero’s outlandish warnings, so she reports him as crazy. The Bad Guys are listening for reports of the Hero, so they attack the hospital next. And so on and so forth.
Obviously, this isn’t how it works. A story is being told, the events have been predecided on, and there is no chance for deviation or choice. A good story has actions flow naturally from previous actions.
Time loops strip that away. Time loops remove the fiction that any character could choose differently than they do. A story in which It Is Written that Neo will turn one way versus another when warned of a vase is a story in which It Is Written that he will succeed at some tasks, fail at others. And because stories exist in universes which survive the Strong Dramatic-Anthropic Principle*, you as a viewer now know exactly what will happen. The spell, for me at least, is broken, and the boom mikes and cameras become visible. The story is revealed as a story, because the author of the story cannot imagine how the world they are presenting actually works.
The only way you can set up a coherent story with stable time loops is with an outside view, being able to see the script as an author. From within a universe, either your own actions aren’t deterministic, and you can’t predict anything about yourself (because you’d have to predict the result of you predicting something, which would require you to predict the result of you predicting the result of your predicting yourself, and so on until you run out of plot-RAM), or your actions are deterministic, and you didn’t set up shit; the script did for you.
So, please no more stable time loops. And if you want to have an oracular character, show us the mechanism for the oracular powers, point out how and where they are incomplete, and have them get something dramatically wrong in accordance with the nature of the powers as you’re setting them up.
*The General Anthropic Principle is that the universe has to be compatible with human life to exist, on account of the fact that a universe incompatible with human life doesn’t have people in it to make up the general anthropic principle. The Dramatic-Anthropic principle is that people tell stories about universes that are interesting to tell stories in; a story that is told to entertain you, by a sentient person with a good model-of-mind and a large budget and crew of editors and involved people, will thus follow some extremely predictable rules of drama.
This is why argument from stories and fictional evidence is so pernicious. In reality, plucky underdogs can be stepped on, races go to the swift, and the Grizzled Highly-Paid Viewer-Identified Male Lead can unceremoniously perish of misfortune in the middle of Act 2.