A bit of invention should help you solve this problem, without needing a physics degree. For example, what if the ring is actually made of billions of bacteria, like the algae blooms that appear in the world's oceans. That way, they might 'migrate' during the year for some reason (eg solar flares, solar/lunar gravitational cycles etc.). Or, a more cliched option, the ring is ancient technology, and it is programmed to move at certain times of the year.

If neither of those take your fancy, you could get a bit more technical: perhaps your planet has an outer atmosphere that has a different chemical composition to Earth's. There might be a layer of gases that is more dense than other gases, but (peculiarly) is also very bouyant. The ring actually its on top of those gases, and so is within the atmosphere, but many kilometres up. For various reasons, the layer of gases moves around in cycles (eg. the same way that hot and cold pressure cells operate in Earth's weather system). It might be like the jet-stream, for example. Correspondingly, the ring, floating on top of the gases, is also carried around the planet when the gases move.

Of course, a chemist or physicist could look at this suggestion and see all the problems wrong with it, but how many of your readers are likely to be chemists or physicists? It just needs to be plausible, not scientifically perfect. It is definitely doable.

Feel free to use any of those ideas, if you want to, or invent some of your own. Good luck with your world.

THW