I tried resetting all of the margins to 2 pt, but that didn't make the problem go away. As a cross-check, I tried setting the "Top Margin" of the "Horizontal" connector to 40 pt, and that didn't make the problem appear.

Something else is wrong.

I appreciate the "Quick Access Toolbar" suggestion, but it really doesn't address the problem. If the overhead of selecting "Rotate Text" were reduced to zero, it wouldn't reduce the work involved in realigning the labels very much at all.

As I said before, I can fix this problem by replacing the misbehaving connectors with new ones if there's no other way to fix it; but I still need to understand what causes it if I'm to prevent it from happening in the future.

The following is a secondary issue, but the "Top Margin" setting is a clumsy way of doing what I use it to do, and even though it's not the cause of the alignment problem I'd be happy to learn about an alternative. In my actual drawing the shapes at the ends of the connectors are often inside other shapes, and I must move the label away from the center of the connector to position it roughly in the middle of the space between the outer shapes. At present I must enter a margin value, see the result, enter another one, etc., until the label is roughly where I want it. I'd much rather be able to click and drag the label to the right position on the connector.