When you edit a symbol, it only changes the symbol for that document - it does not save the edits to the original symbol file in the common library.
There are two ways to edit a symbol and have the changes update the Common Library:
(1) edit the original symbol file (e.g., "symbol.graphic.png" from the Common Library folder) then save the file directly back to that location with the same filename (WARNING: if it is a component symbol with properties that can be edited in the Symbol Properties Panel, it is very easy to break the symbol but changing it's object and layer structure. The editable properties depend on the object and layer names - change those, and the editable symbol will no longer work.)
(2) open a copy of the symbol you want to change, right-click and choose "Symbol > Break Apart" to turn it into a regular graphic object no longer connected to the Common Library, edit the graphics as desired, then select all of the parts and press F8 ("Create New Symbol") - save the updated symbol to the Common Library and give it a new name so that you know which is your edited version. (WARNING: if this was a component symbol with editable properties, it will lose that editability when you break it apart and re-save it. You'll need to use the Command > Create Symbol Script to make the symbol customizable again.)
Thank you Dave. That did the trick. I wish it said that in "Adobe Fireworks CS4 Classroom in a Book" instead of the way it describe symbol editing on p.206.