Thanks for the detailed explanation.
To clarify and make sure: *Does* the Blackberry actually have 10.3.2.556 on it, at present? as opposed to what the software says.
I suggest that you try this:
1. uninstall the Blackberry Link software (provided you have a reinstall source)
2. restart your computer
3. reinstall the BlackBerry Link software after that.
That may reinitialize the connection, or the upgrade status, or whatever it was that went wrong, and clear up the apparent deadlock. Provided that you follow instructions when you try to do the update again, to the letter... lest the situation somehow repeat itself through an 'operator error'... I'm just trying to cover all possible sources of this bothersome error condition, and propose that we go at it cautiously and carefully.