I'm attaching a new version of the file in which the "tilted" connector's label has the default top margin, and the "horizontal" connector's label has a top margin set to 40 pt. On my system the "tilted" label is still tilted, and the "horizontal" label is still horizontal.
Thank you for pointing out the little yellow icon (really invisible unless one knows to look for it). Note that the "horizontal" connector has one, but the "tilted" connector does not. This is probably a clue to what is wrong, but my knowledge of Visio is not deep enough to suggest what it means.
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