may be its rodents stripping the bark off those branches, or a cat using it as a scratching post, i would put some chicken wire or something similar around the base and see if it stops
Exactly my thinking. I had this happen to both my Eureka lemon and what I think is a Valencia orange tree. It nearly killed them both. I am sure it is due to either ground squirrels or roof rats. The only way to keep the squirrels and rats out of the trees is to trap them. At least so far, this has been my only option. Can't poison them because I've got a dog and I'm afraid the dog might get to a weakened rat or squirrel. Or, a hawk or owl might pick up a poisoned rat or squirrel and succumb.