The Cyclamen has in fact been successfully rebloomed. (It even has more blooms on it than it did when I bought it!) So it can be done.
The plant still makes me kind of nervous -- I'm afraid that at any moment it's going to fall to pieces and I won't know why -- but I never expected to get this far with it, so I'm feeling a sort of anxious pride about this.
Not that I ever feel any other kind of pride, it should be noted.