Minecraft wiki entry for Block_entity, associated text: The beacon and end gateway beams stop rendering beyond 256 blocks or when the end gateway is out of frame.
The contents of a campfire stop rendering beyond 64 blocks.
The book on a lectern stops rendering beyond 64 blocks.
The mob inside a spawner stops spinning beyond the  RequiredPlayerRange, which is 16 blocks by default, and stops rendering beyond 64 blocks.
The note particles emitted by a note block stop rendering beyond 32 blocks.
Pistons stop animating beyond 64 blocks.
The book on an enchanting table stops rendering beyond 64 blocks.
The outlines created by a structure block stop rendering beyond 96 blocks.
The bell part of the model of a bell, but not the frame, stops rendering beyond 64 blocks.