The answer? It depends!
If you tone to
completion, you need not re-fix.
If you do not completely tone, there remains in the print some re-halogenated silver salts that have not been fully developed out to something more stable. If you leave those salts in the print, it will deteriorate over time.
A further fix will convert those salts into a water soluble complex that you can wash away (sound familiar?).
I do a fair amount of partial and split toning. Sometimes, if I am using an incomplete bleach to help control the results, the final change in tone is very subtle. It can be hard to tell the difference between complete toning after a light bleach and incomplete toning. So it is a good idea to make a fix step a regular part of your routine.
I also like to use hardener after toning, because toned emulsions can be somewhat fragile. If you use hardening fixer as the final pre-wash step, it will accomplish both purposes (but extend your final wash).