I understand what Maja is saying about the use of the term "dealbreaker." Remember, she's a linguist, so thinks about these things in a way the rest of us may not. Like Laura Vishoot, I tend to use dealbreaker to mean something that will simply end my consideration of or participation in a particular situation, and this difference in interpretation probably reflects our use of English vs Maja's.
With respect to dogs, I have been the recipient of dogs who were moved on. Yes, they had baggage they brought with them from their previous situations, but the "deal" I made when I took them was that I would work within or through that baggage.
I tend to hang on to dogs who don't suit me longer than maybe I should. In most cases, it's because I really worry about what will become of them if I move them on. Maybe it's controlling; maybe it's a pet mentality, but considering what I know of the working stockdog world, I personally can't just sell a dog on without careful consideration about where that dog will go and where it might end up on down the line.
That said, I have rehomed several dogs. The "dealbreakers" were (1) you don't get to attack and maim my oldsters, (2) I really don't like working a dog I have to micromanage because that doesn't fit my work situation at home (this was a good dog, fully trained although not solid on the shed, and I sent him to an active pet home on a recommendation from another handler who knew the person well, but also because I knew he wouldn't get passed on beyond that), (3) a youngster who has potential but who has some behavioral characteristics that drive me nuts (and in this case money is a consideration, but it makes me no less concerned about this fellow's ultimate fate).
I keep my old dogs because they are dogs who have worked hard for me and I personally feel that the covenant I make with them is that they *can* live out their lives with me after having given me the best part of theirs. Than again, my first open dog became mine because her owner was willing to let her go (after meeting me and realizing I would be a great place for the dog), so I have benefited from that side of the equation as well. I continue to use my dogs at home as long as they're capable. Running a large open course may become more difficult for the 11 year olds, but they can still manage to work at home (and set out if the days aren't super long or super miserable weatherwise). When realistically they've got just a few years left, I don't see the point in rehoming them (i.e., there's a difference between retiring a 6-8 year old--the age at which Jill came to me--to an easier working situation and retiring an 11-12 year old to such a situation).
A novice could learn from Pip, but I suspect he's beginning to go deaf at nearly 11, so his usefulness in training a novice handler would be limited (not to mention I can't imagine sending him anywhere). That said, if someone comes here for lessons, I'll let them work a retiree or near retiree to help illustrate a point in training and I will let my neighbors borrow them for chores here at the farm.
Anyway, I think from a semantics viewpoint, the use of the term dealbreaker is an interesting one.