If the resulting liquid is acidic, Sulfur Dioxide will form and leave the solution (c.f. smell of rotten eggs).
Actually SO2 is a choking sort of odor - I describe it as making you want to cough, but if you do the cough is not satisfying. The rotten egg odor is hydrogen sulfide.
It has been described in scientific literature, though, e.g. The Stability of Concentrated Thiosulphate Solutions at High Temperature. Part II: The Loss of Sulphite, by E. R. Brumpton and G. I. P. Levenson, in The Journal of Photographic Science, vol 13, p 79ff. The attached graph shows this effect including the increase in thiosulfate concentration during fixer decay.
I've done that same sort of analysis (minus the sulfate) hundreds and hundreds of times, although mostly on paper blix. But still, I've done studies during electrolytic desilvering of C-41 fixer, watching the sulfite concentration go down (it's "consumed" at the anode). I'm accustomed to seeing the thiosulfate level stay almost constant throughout the process. It's curious to me that it actually increased during the test. I was wondering, what on earth are they testing? It's not the 58-60% ammonium thiosulfate cuz that doesn't contain any appreciable sulfite. But it has a thiosulfate level way higher than a fixer solution, and a similarly high sulfite concentration. So it occurs to me that perhaps this test was of a rapid fixer concentrate - the sort of thing that a photographer might purchase, and the high temperature, whatever it was, was intended to simulate accelerated aging. So I wonder if the increase in thiosulfate was an artifact of the concentrated mix or high temperature.
Again, I've never seen thiosulfate levels change appreciably - as it degrades it is essentially regenerated by sulfite. However, I haven't specifically studied stagnant fixer - I've done this as part of controlling and improving processes for a large finishing operation; we never just let fixer sit around unused. We replenished everything and when volume went down, well, you just mix less replenisher. But... It's been pretty clear that our fixer never went bad when it had adequate sulfite levels. I can only think of a time or two when we had fixer sulfurize, and that's when someone had somehow screwed up and left a "small" tank isolated for months. One might say that, well, you never had fixer get old. And that's somewhat true for C-41 (it can't be regenerated, at least not easily). But with paper blix, it was constantly regenerated at a high reuse level, so it's likely that some of the thiosulfate molecules, or at least parts of them, had been in there for years. But that fixer, in the blix, never "came apart."
Ps, I would concur with Rudi that the preferred way to raise pH of an ammonium thiosulfate fixer is with ammonium hydroxide. But I wouldn't worry too much about moderate quantities of sodium hydroxide either. After all, the normal method of getting sulfite ion is with sodium sulfite, so there is already some sodium ion in there. As far as I know this is not especially problematic.
Btw, both of those chemicals need to be handled with care, and I mean that the user needs to have appropriate protection AND know what they're gonna do in case of a spill. But the ammonium hydroxide is, imo, far more of an irritant. If you were to spill, say a full gallon in your darkroom, it would probably drive everyone out of your house. And I don't know how you'd get back in to clean it up unless you had a full-face respirator with ammonia cartridges in it. With just a half-mask respirator your eyes would be so irritated and watering so bad you probably couldn't find your way in. I don't say this often, but I don't think it's something a "regular person" should be handling, except maybe in small quantities.