I get this same issue. Tying leads to posts for more then a minute is useless. I suspect the chunk loading causes the mob to temporarily "fall" more than 10 blocks from the lead triggering it to break. If you remember back when there were missing chunk bugs you'd often catch mobs "bouncing" up and down in the missing space. They keep falling and resetting their position until the blocks load. My guess is that's what happens and snaps the lead.
Alex Ford
I get this same issue. Tying leads to posts for more then a minute is useless. I suspect the chunk loading causes the mob to temporarily "fall" more than 10 blocks from the lead triggering it to break. If you remember back when there were missing chunk bugs you'd often catch mobs "bouncing" up and down in the missing space. They keep falling and resetting their position until the blocks load. My guess is that's what happens and snaps the lead.