When an entity gets more than about 80* blocks away from the player, it becomes invisible. This is normal Minecraft behaviour, but the problem is that if an entity is too far away while the recording, then the entity will be invisible in the Replay as well even if you get closer with the camera. It also appears to be a problem with block entities, like chests not showing their opening animation if they get opened by someone else while the person recording is too far away. This will also be the case when you render a video.
* This number was found on a singleplayer world with OptiFine, it may be different depending on the circumstances.
Method to reproduce:
1. Open a world to record a Replay.
2. Summon an entity, preferably one with no AI so it doesn't move.
3. Move a bit less than 80 blocks away. The entity is still visible.
4. Move a bit farther away until the entity becomes invisible.
5. Exit the world and open the Replay file that was just recorded.
6. Stay close to the entity you spawned while the player walks away from the entity. Notice that the moment the player moved too far away from the entity, the entity becomes invisible, even though the camera is still close to the entity.