I have a 16-inch, Nov 2023 MacBook Pro. I've run every version of macOS up to version 15.1, as well as nearly every version of visionOS up to version 2.1. At some point in the last few months the screen mirroring stopped working smoothly and now continually pauses from time to time. Similar to how @Paulie54 has described, though I find that the session can usually recover on its own after some time. I have not seen any improvement in all the OS versions tried.
Given that I have the latest version of both OSs as of October 9, 2024, the highest performing MacBook Pro currently available, and the desktop mirroring feature previously worked without issue I can conclude that a failure to upgrade the OS or the hardware is the root cause. I can also confirm that my laptop is plugged in and turned on, and that both my laptop and my Vision Pro seems to work fine in all other respects, so it seems unlikely that generic trouble shooting advice will be helpful.
Perhaps someone with specific information on this issue will be able to provide more useful guidance