I have my frame rate match and dynamic range match set to “on”. That means that once playback begins, there’s a brief disconnection as the display and atv renegotiate hdmi info and hdcp encryption again.
I think what is happening is that this, in turn, triggers the pause on Apple TV side.
I recently changed my hardware configuration (different tv) which might mean the delay might be a tad longer - causing the pause to stick.
This explains why the issue is not consistent on all content - it depends on the rate and range for the time duration of the renegotiation.
I tested the theory and turned off the match rate and the issue was fine until I tuned it back on.
I switched to 4:2:0 - issue seems to be almost gone because the sync time on it is slightly faster. Must be fast enough to prevent atv from going into mousse mode.
If you changed the device chain (HDMI cable, TV, AV receiver, etc…) it can sometimes help to reset the Apple TV video settings (in Apple TV Settings > Video and Audio) and set things up again the way you want them.