Leashes break when moving far from leash point.   Appears to be related to leashes where the leash point (a fence post) is in a different chunk from the leashed creature (in this case a horse).

Moving far away from the leash point (the side that the horse is) seems to break the leash, and drop it as an item.  

I have a stable area with two lines of horses tied to fence posts.   The line of horses where the horse and the leash tie point are in the same chunk are fine.  The line of horses where the horse is obliged by the scenery to stand in a different chunk to its leashed fence post consistently show the issue.

If I return immediately, the leash is floating as if dropped as an item.  If I do not return immediately, the leash de-spawns as one might expect.   As a result, my leashes are getting destroyed, and my horses are wandering.

At a guess, when I am moving away and the chunk with the fence post gets unloaded, but the chunk with the horse is still loaded, the horse appears to have a leash, but not apparently leashed to anything, so the leash is detached from the horse and dropped as an item.