I tried creating a simple example, and it didn't exhibit the problem. The labels began life horizontal, and stayed horizontal no matter what happened to the connector's slope.
I created a simplified version of one of my actual drawings which did exhibit the problem. There is one sheet with two shapes and a connector; move either shape and you'll see the orientation of the connector's label change.
Most interesting, when I added new shapes and connectors to the drawing that exhibits the problem, they did not exhibit the problem.
So there's something about the connectors in my existing drawings that causes the problem.
Fixing the problem by hand (replacing the old connectors and/or shapes with new ones) is a manageable solution, provided I know how to prevent the problem from recurring.
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