Stop killing yourself!
While I was off clearing out a mine in Skyrim I got the message that my dog companion had gone home. Your followers tend to leave if you keep them waiting somewhere for a few days. Part of me wanted the dog to leave me alone for a bit so that I could use another animal follower but I just couldn't tell him to go away because he whimpered before leaving.
Come back, I didn't mean it!
Also because he's originally a stray and doesn't have another home I wouldn't know where to find him again.
So with this in mind I thought I'd tell him to wait at my home in Whiterun and then when he stopped being my "official" animal companion he would hopefully just stay there as if that was his home.
Having got the message that he'd waited around long enough I took a carriage back to Breezehome to see if he was still there and... He was!
His home is my home and now I don't have to order him about any more. He can just sneak up behind me whenever he wants.
And look at that cat! Typical feline. It smells someone cooking and it's
instantly there wanting some!