When you screen share to another Mac, and then minimize the screen share window to the Dock, it appears to “pause” until you un-hide the window.
(The easiest way to see this is if you have the clock in your menubar and minimize the window for several minutes. When you un-hide the window, the clock will be several minutes slow at first, but will quickly catch up. I noticed this while over a high-latency satellite Internet connection, which may have made the update lag more noticeable.
I assume that this is done for bandwidth and/or CPU savings. If the window is minimized, obviously it isn’t in use and therefore doesn’t need to be updated. Even over my slow Internet connection, the update was pretty quick.