A more pressing concern is that sulfite is commonly and cheaply available as the sodium salt, and you ideally don't want to use that to recover a decaying rapid/ammonium fixer as it'll slow the fixer down considerably. The solution is to purchase ammonium sulfite, but in consumer/hobby quantities this likely is more expensive than just getting some new fixer.
In the realm of film fixers (prev post was mostly RA-4 PAPER process) I don't see the use of the sodium sulfite in the fixer as much of a problem. There is a relatively minor amount compared to, for example, the amount of sodium that would be used in a non-rapid style sodium thiosulfate fixer.
As an example see Kodak's H24 Motion picture manual. (Should be available on the internet.) In module 07, page 7-33, a formula is given for fixer. In a "fresh tank" the formula is, roughly, ammonium thiosulfate (58% solution) = 185 mL/L, then two forms of sulfite ion. They are: sodium sulfite = 10 g/L, and sodium metabisulfite = 8.4 g/L.
So the preservatives are both using sodium, whereas the fixing agent is ammonium thiosulfate. I went through and estimated the relative amount of sodium in the preservative package, compared to how much sodium would come into play if SODIUM thiosulfate (slow fixer) had been used.
For the Kodak ECN fixer I estimate that the 10 grams sodium sulfite divided by the molecular weight of 126 grams =~ 0.08 moles. But... since each molecule contains TWO sodium atoms this gives 2 x 0.08 = 0.16 moles of sodium per liter. In a similar manner the sodium bisulfite gives a further 0.09 moles of sodium, for a total around 0.25 moles sodium in the ECN fixer. Now the question is, how significant is that, compared to if the fixing agent = SODIUM thiosulfate?
I estimate the ammonium thiosulfate used to be very close to 1 mole per liter. So a straight up change to SODIUM thiosulfate, with TWO sodiums per molecule, would have close to 2 moles of sodium. This is compared to only 0.25 moles sodium coming from the preservatives (sulfite). In other words the use of sodium sulfite in a rapid fixer (ammonium thiosulfate based) is only about 1/8 the sodium content if the fixer had been based on sodium thiosulfate. So it seems silly to say that adding more sodium sulfite to the rapid fixer is gonna bring it down to the level of an old style sodium thiosulfate fixer.
I don't know how clear this is to the "typical" reader who might be following this,, so let me just repeat that the Kodak motion picture manuals, which would be used by any lab mixing their chemicals from components, do not seem to have a problem using sodium sulfite, ie, adding sodium ion, to their rapid fixers.
So I personally do not see much problem putting more sodium ion, in the form of sodium sulfite, into a rapid fixer as a means of saving it from a collapse of the thiosulfate (sulfuring out). From a gut feeling I have the sense that simply using a fixer, where the silver concentration is increasing, would have a larger effect on the fixing speed than a moderate amount of sodium ion added. But... I have never specifically tested for this. My experience has been primarily based on following the specifications of the manufacturer with respect to time and temperature, etc., and to confirm that the chemical functions are comfortably completed within that time window. And... we made sure that the chemicals remained within "normal" analytical specs. So again, I've never actually "saved" a fixer during a "sulfuring out" failure cuz we never allowed the fixer to get that far.
Yeah, which is what I've done [adding sulfite to a fixer which has started to sulfurize], but it's only marginally effective and offers only a slight delay of the inevitable.
All I can say is that this is contrary to what I think I know. My guess would be that you didn't add enough. Perhaps the sulfuring out was so advanced that the additional sulfite was not enough. Or that perhaps, for some reason, the solution pH had gotten too low. I would guess, that had a sulfite analysis been done, that it would have been back down to zilch again.
To me it would've been a fun thing to investigate back in the day. I have little doubt that we would have gotten to the bottom of it. Perhaps not us directly - I don't understand the deep down chemistry - but Kodak would have connected us with their knowledgeable people, or perhaps some other alternative source. But those days are long gone.
I'm still gonna believe more sulfite would have stopped the collapse of the thiosulfate unless I hear of 2 or 3 more people who tried and failed. Then the issue will sit in the back burner of my mind until... who knows?