You say that he is always supervised, but allowed to go everywhere. Have you checked behind your couches, etc...? Under beds? Behind trash cans? Do you see him every moment? Are you never distracted?
I ask because my dogs are always getting into stuff and I limit where they go in the house. There are things that they get into that you won't even think about. Honestly!
Mine almost died once because of a used medication patch that we didn't know was under a bed!
At the very least, I would tether him to you. I did that with Gizmo and it made all of the difference. He was always close to me attached by a leash.

They really want to be beside/with you more than anything else.
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The fullness of our heart is expressed in our eyes, in our touch, in what we write, in what we say, in the way we walk, the way we receive, the way we need. -Mother Teresa (
RIP Gizmo 3/9/07-8/18/12)