Quick Parts stop updating if a document is moved to a different library, they show the last value of the original library but stop updating. If you have heavily used Quick Parts for things like "Version Number" and "Document ID" you might be thinking that the Update Document action was going to solve your problems (e.g. put this step in just before the document is approved to make sure a document that have been moved reconnects to their columns)... and this is true EXCEPT if your column name has a space in it.